Question

a
multiply.

1. $2x^2 + 4x + 16$ and $3x - 4$
2. $3y^2 - 3y + 9$ and $2y + 3$
3. $4a^2b - 2ab + 3b^2$ and $ab - 2b + 1$
4. $2x^2 + y^2 - 2xy$ and $x^2 - 2y^2 - xy$
5. $(a - b)(a^2 + ab + b^2)$
6. $(t + 1)(t^2 - t + 1)$
7. $(2x + 3y)(2x + y)$
8. $(2a - 3b)(2a - b)$
9. $left(4x^2 - \frac{1}{2}y

ight)left(3x + \frac{1}{4}y
ight)$

1. $left(2y^3 + \frac{1}{5}x

ight)left(3y - \frac{1}{4}x
ight)$

1. $(2x^2 - y^2)(2x - 2y)$
2. $(3y^2 - 2)(3y - x)$
3. $(2x + 3y)^2$
4. $(5x + 2y)^2$
5. $(2x^2 - 3y)^2$
6. $(4x^2 - 5y)^2$
7. $(2x^3 + 3y^2)^2$
8. $(5x^3 + 2y^2)^2$
9. $(3x - 2y)(3x + 2y)$
10. $(3x + 5y)(3x - 5y)$
11. $(x^2 + yz)(x^2 - yz)$
12. $(2x^2 + 5y)(2x^2 - 5y)$
13. $(3x^2 - 2)(3x^2 + 2)$
14. $(5x^2 - 3)(5x^2 + 3)$
15. $(y + 5)^3$
16. $(t - 7)^3$
17. $(m^2 - 2n)^3$
18. $(2f + 3d)^3$

multiplication of polynomials

Explanation:

Step1: Distribute each term of first polynomial

$3x(2x^2 + 4x + 16) - 4(2x^2 + 4x + 16)$

Step2: Expand each product

$6x^3 + 12x^2 + 48x - 8x^2 - 16x - 64$

Step3: Combine like terms

$6x^3 + (12x^2-8x^2)+(48x-16x)-64$
$6x^3 + 4x^2 + 32x - 64$

---

Step1: Distribute each term of first polynomial

$2y(3y^2 - 3y + 9) + 3(3y^2 - 3y + 9)$

Step2: Expand each product

$6y^3 - 6y^2 + 18y + 9y^2 - 9y + 27$

Step3: Combine like terms

$6y^3 + (-6y^2+9y^2)+(18y-9y)+27$
$6y^3 + 3y^2 + 9y + 27$

---

Step1: Distribute each term of first polynomial

$ab(4a^2b - 2ab + 3b^2) -2b(4a^2b - 2ab + 3b^2) +1(4a^2b - 2ab + 3b^2)$

Step2: Expand each product

$4a^3b^2 - 2a^2b^2 + 3ab^3 -8a^2b^2 +4ab^2 -6b^3 +4a^2b -2ab +3b^2$

Step3: Combine like terms

$4a^3b^2 + (-2a^2b^2-8a^2b^2)+3ab^3 +4a^2b +4ab^2 +(-6b^3+3b^2)-2ab$
$4a^3b^2 -10a^2b^2 + 3ab^3 + 4a^2b + 4ab^2 -6b^3 +3b^2 -2ab$

---

Step1: Distribute each term of first polynomial

$x^2(2x^2 + y^2 - 2xy) -2y^2(2x^2 + y^2 - 2xy) -xy(2x^2 + y^2 - 2xy)$

Step2: Expand each product

$2x^4 + x^2y^2 -2x^3y -4x^2y^2 -2y^4 +4xy^3 -2x^3y -xy^3 +2x^2y^2$

Step3: Combine like terms

$2x^4 + (-2x^3y-2x^3y)+(x^2y^2-4x^2y^2+2x^2y^2)+(4xy^3-xy^3)-2y^4$
$2x^4 -4x^3y -x^2y^2 +3xy^3 -2y^4$

---

Step1: Distribute binomial over trinomial

$a(a^2 + ab + b^2) -b(a^2 + ab + b^2)$

Step2: Expand each product

$a^3 + a^2b + ab^2 -a^2b -ab^2 -b^3$

Step3: Combine like terms

$a^3 + (a^2b-a^2b)+(ab^2-ab^2)-b^3$
$a^3 - b^3$

---

Step1: Distribute binomial over trinomial

$t(t^2 - t + 1) +1(t^2 - t + 1)$

Step2: Expand each product

$t^3 -t^2 +t +t^2 -t +1$

Step3: Combine like terms

$t^3 + (-t^2+t^2)+(t-t)+1$
$t^3 + 1$

---

Step1: Use FOIL method

$(2x)(2x) + (2x)(y) + (3y)(2x) + (3y)(y)$

Step2: Calculate each product

$4x^2 + 2xy + 6xy + 3y^2$

Step3: Combine like terms

$4x^2 + 8xy + 3y^2$

---

Step1: Use FOIL method

$(2a)(2a) + (2a)(-b) + (-3b)(2a) + (-3b)(-b)$

Step2: Calculate each product

$4a^2 -2ab -6ab +3b^2$

Step3: Combine like terms

$4a^2 -8ab +3b^2$

---

Step1: Distribute each term of first binomial

$4x^2(3x + \frac{1}{4}y) - \frac{1}{2}y(3x + \frac{1}{4}y)$

Step2: Expand each product

$12x^3 + x^2y - \frac{3}{2}xy - \frac{1}{8}y^2$

Step3: No like terms to combine

(No further expression needed)

---

Step1: Distribute each term of first binomial

$2y^3(3y - \frac{1}{4}x) + \frac{1}{5}x(3y - \frac{1}{4}x)$

Step2: Expand each product

$6y^4 - \frac{1}{2}xy^3 + \frac{3}{5}xy - \frac{1}{20}x^2$

Step3: No like terms to combine

(No further expression needed)

---

Step1: Distribute each term of first polynomial

$2x^2(2x - 2y) - y^2(2x - 2y)$

Step2: Expand each product

$4x^3 -4x^2y -2xy^2 +2y^3$

Step3: No like terms to combine

(No further expression needed)

---

Step1: Distribute each term of first polynomial

$3y^2(3y - x) -2(3y - x)$

Step2: Expand each product

$9y^3 -3xy^2 -6y +2x$

Step3: No like terms to combine

(No further expression needed)

---

Step1: Use square of binomial formula

$(a+b)^2 = a^2 + 2ab + b^2$, where $a=2x, b=3y$

Step2: Substitute and calculate

$(2x)^2 + 2(2x)(3y) + (3y)^2$
$4x^2 +12xy +9y^2$

---

Step1: Use square of binomial formula

$(a+b)^2 = a^2 + 2ab + b^2$, where $a=5x, b=2y$

Step2: Substitute and calculate

$(5x)^2 + 2(5x)(2y) + (2y)^2$
$25x^2 +20xy +4y^2$

---

Step1: Use square of binomial formula

$(a-b)^2 = a^2 - 2ab + b^2$, where $a=2x^2, b=3y$

Step2: Substitute and calculate

$(2x^2)^2 - 2(2x^2)(3y) + (3y)^2$
$4x^4 -12x^2y +9y^2$

---

Step1: Use square of binomial formula

$(a-b)^2 = a^2 - 2ab + b^2$, where $a=4x^2, b=5y$

Step2: Substitute and calculate

$(4x^2)^2 - 2(4x^2)(5y) + (5y)^2$
$16x^4 -40x^2y +25y^2$

---

Step1: Use square of binomial formula

$(a+b)^2 = a^2 + 2ab + b^2$, where $a=2x^3, b=3y^2$

Step2: Substitute and calculate

$(2x^3)^2 + 2(2x^3)(3y^2) + (3y^2)^2$
$4x^6 +12x^3y^2 +9y^4$

---

Step1: Use square of binomial formula

$(a+b)^2 = a^2 + 2ab + b^2$, where $a=5x^3, b=2y^2$

Step2: Substitute and calculate

$(5x^3)^2 + 2(5x^3)(2y^2) + (2y^2)^2$
$25x^6 +20x^3y^2 +4y^4$

---

Step1: Use difference of squares formula

$(a-b)(a+b)=a^2-b^2$, where $a=3x, b=2y$

Step2: Substitute and calculate

$(3x)^2 - (2y)^2$
$9x^2 -4y^2$

---

Step1: Use difference of squares formula

$(a-b)(a+b)=a^2-b^2$, where $a=3x, b=5y$

Step2: Substitute and[LLM SSE On Failure]

Answer:

Step1: Distribute each term of first polynomial

$3x(2x^2 + 4x + 16) - 4(2x^2 + 4x + 16)$

Step2: Expand each product

$6x^3 + 12x^2 + 48x - 8x^2 - 16x - 64$

Step3: Combine like terms

$6x^3 + (12x^2-8x^2)+(48x-16x)-64$
$6x^3 + 4x^2 + 32x - 64$

---

Step1: Distribute each term of first polynomial

$2y(3y^2 - 3y + 9) + 3(3y^2 - 3y + 9)$

Step2: Expand each product

$6y^3 - 6y^2 + 18y + 9y^2 - 9y + 27$

Step3: Combine like terms

$6y^3 + (-6y^2+9y^2)+(18y-9y)+27$
$6y^3 + 3y^2 + 9y + 27$

---

Step1: Distribute each term of first polynomial

$ab(4a^2b - 2ab + 3b^2) -2b(4a^2b - 2ab + 3b^2) +1(4a^2b - 2ab + 3b^2)$

Step2: Expand each product

$4a^3b^2 - 2a^2b^2 + 3ab^3 -8a^2b^2 +4ab^2 -6b^3 +4a^2b -2ab +3b^2$

Step3: Combine like terms

$4a^3b^2 + (-2a^2b^2-8a^2b^2)+3ab^3 +4a^2b +4ab^2 +(-6b^3+3b^2)-2ab$
$4a^3b^2 -10a^2b^2 + 3ab^3 + 4a^2b + 4ab^2 -6b^3 +3b^2 -2ab$

---

Step1: Distribute each term of first polynomial

$x^2(2x^2 + y^2 - 2xy) -2y^2(2x^2 + y^2 - 2xy) -xy(2x^2 + y^2 - 2xy)$

Step2: Expand each product

$2x^4 + x^2y^2 -2x^3y -4x^2y^2 -2y^4 +4xy^3 -2x^3y -xy^3 +2x^2y^2$

Step3: Combine like terms

$2x^4 + (-2x^3y-2x^3y)+(x^2y^2-4x^2y^2+2x^2y^2)+(4xy^3-xy^3)-2y^4$
$2x^4 -4x^3y -x^2y^2 +3xy^3 -2y^4$

---

Step1: Distribute binomial over trinomial

$a(a^2 + ab + b^2) -b(a^2 + ab + b^2)$

Step2: Expand each product

$a^3 + a^2b + ab^2 -a^2b -ab^2 -b^3$

Step3: Combine like terms

$a^3 + (a^2b-a^2b)+(ab^2-ab^2)-b^3$
$a^3 - b^3$

---

Step1: Distribute binomial over trinomial

$t(t^2 - t + 1) +1(t^2 - t + 1)$

Step2: Expand each product

$t^3 -t^2 +t +t^2 -t +1$

Step3: Combine like terms

$t^3 + (-t^2+t^2)+(t-t)+1$
$t^3 + 1$

---

Step1: Use FOIL method

$(2x)(2x) + (2x)(y) + (3y)(2x) + (3y)(y)$

Step2: Calculate each product

$4x^2 + 2xy + 6xy + 3y^2$

Step3: Combine like terms

$4x^2 + 8xy + 3y^2$

---

Step1: Use FOIL method

$(2a)(2a) + (2a)(-b) + (-3b)(2a) + (-3b)(-b)$

Step2: Calculate each product

$4a^2 -2ab -6ab +3b^2$

Step3: Combine like terms

$4a^2 -8ab +3b^2$

---

Step1: Distribute each term of first binomial

$4x^2(3x + \frac{1}{4}y) - \frac{1}{2}y(3x + \frac{1}{4}y)$

Step2: Expand each product

$12x^3 + x^2y - \frac{3}{2}xy - \frac{1}{8}y^2$

Step3: No like terms to combine

(No further expression needed)

---

Step1: Distribute each term of first binomial

$2y^3(3y - \frac{1}{4}x) + \frac{1}{5}x(3y - \frac{1}{4}x)$

Step2: Expand each product

$6y^4 - \frac{1}{2}xy^3 + \frac{3}{5}xy - \frac{1}{20}x^2$

Step3: No like terms to combine

(No further expression needed)

---

Step1: Distribute each term of first polynomial

$2x^2(2x - 2y) - y^2(2x - 2y)$

Step2: Expand each product

$4x^3 -4x^2y -2xy^2 +2y^3$

Step3: No like terms to combine

(No further expression needed)

---

Step1: Distribute each term of first polynomial

$3y^2(3y - x) -2(3y - x)$

Step2: Expand each product

$9y^3 -3xy^2 -6y +2x$

Step3: No like terms to combine

(No further expression needed)

---

Step1: Use square of binomial formula

$(a+b)^2 = a^2 + 2ab + b^2$, where $a=2x, b=3y$

Step2: Substitute and calculate

$(2x)^2 + 2(2x)(3y) + (3y)^2$
$4x^2 +12xy +9y^2$

---

Step1: Use square of binomial formula

$(a+b)^2 = a^2 + 2ab + b^2$, where $a=5x, b=2y$

Step2: Substitute and calculate

$(5x)^2 + 2(5x)(2y) + (2y)^2$
$25x^2 +20xy +4y^2$

---

Step1: Use square of binomial formula

$(a-b)^2 = a^2 - 2ab + b^2$, where $a=2x^2, b=3y$

Step2: Substitute and calculate

$(2x^2)^2 - 2(2x^2)(3y) + (3y)^2$
$4x^4 -12x^2y +9y^2$

---

Step1: Use square of binomial formula

$(a-b)^2 = a^2 - 2ab + b^2$, where $a=4x^2, b=5y$

Step2: Substitute and calculate

$(4x^2)^2 - 2(4x^2)(5y) + (5y)^2$
$16x^4 -40x^2y +25y^2$

---

Step1: Use square of binomial formula

$(a+b)^2 = a^2 + 2ab + b^2$, where $a=2x^3, b=3y^2$

Step2: Substitute and calculate

$(2x^3)^2 + 2(2x^3)(3y^2) + (3y^2)^2$
$4x^6 +12x^3y^2 +9y^4$

---

Step1: Use square of binomial formula

$(a+b)^2 = a^2 + 2ab + b^2$, where $a=5x^3, b=2y^2$

Step2: Substitute and calculate

$(5x^3)^2 + 2(5x^3)(2y^2) + (2y^2)^2$
$25x^6 +20x^3y^2 +4y^4$

---

Step1: Use difference of squares formula

$(a-b)(a+b)=a^2-b^2$, where $a=3x, b=2y$

Step2: Substitute and calculate

$(3x)^2 - (2y)^2$
$9x^2 -4y^2$

---

Step1: Use difference of squares formula

$(a-b)(a+b)=a^2-b^2$, where $a=3x, b=5y$

Step2: Substitute and[LLM SSE On Failure]