Question

continued from previous page
when multiplying a negative monomial by a polynomial, the negative monomial will change the sign of every term.

examples find each product.
c. $(6a^{2}-2b^{2}+c)(-4)$
$(6a^{2}-2b^{2}+c)(-4)$
$6a^{2}(-4)-2b^{2}(-4)+c(-4)$
$-24a^{2}+8b^{2}-4c$
$longleftrightarrow \text{distribute and simplify.} \longrightarrow$
d. $-3t^{2}(t^{2}-5t+2)$
$-3t^{2}(t^{2}-5t+2)$
$t^{2}(-3t^{2})-5t(-3t^{2})+2(-3t^{2})$
$-3t^{4}+15t^{3}-6t^{2}$

find each product.

1. $(x + 9)(5)$
2. $2x(x^{2}-6x + 3)$
3. $-4x(x^{2}+8)$
4. $(5 - x^{2}+2)(-3)$
5. $2a^{2}(5b^{2}+3ab + 6a + 1)$
6. $(3x^{2}+6x - 5)(-3x)$

Explanation:

Step1: Distribute 5 to each term

$x(5) + 9(5)$

Step2: Simplify the products

$5x + 45$

---

Step1: Distribute $2x$ to each term

$2x(x^2) + 2x(-6x) + 2x(3)$

Step2: Simplify the products

$2x^3 - 12x^2 + 6x$

---

Step1: Distribute $-4x$ to each term

$-4x(x^2) + (-4x)(8)$

Step2: Simplify the products

$-4x^3 - 32x$

---

Step1: Combine like terms first

$(7 - x^2)(-3)$

Step2: Distribute $-3$ to each term

$7(-3) - x^2(-3)$

Step3: Simplify the products

$-21 + 3x^2$

---

Step1: Distribute $2a^2$ to each term

$2a^2(5b^2) + 2a^2(3ab) + 2a^2(6a) + 2a^2(1)$

Step2: Simplify the products

$10a^2b^2 + 6a^3b + 12a^3 + 2a^2$

---

Step1: Distribute $-3x$ to each term

$3x^2(-3x) + 6x(-3x) - 5(-3x)$

Step2: Simplify the products

$-9x^3 - 18x^2 + 15x$

Answer:

1. $5x + 45$
2. $2x^3 - 12x^2 + 6x$
3. $-4x^3 - 32x$
4. $3x^2 - 21$
5. $10a^2b^2 + 6a^3b + 12a^3 + 2a^2$
6. $-9x^3 - 18x^2 + 15x$