Question

name: date: va valentines multiplying polynomials color by number directions: answer the question. use your answer to find the color that will be used for each number on the following page. 1. $2xy(3xy) =$ 2. $a(a + 3) =$ 3. $(t + 4)(t - 1) =$ $5x^2y^2$ purple $6x^2y^2$ dk. blue $5xy^2$ black $a^2 + 3$ green $a^2 + 9$ blue $a^2 + 3a$ black $t^2 + 3t - 4$ blue $t^2 + 3t$ red $t^2 + 5t - 4$ green 4. $(x + 2)(x - 2) =$ 5. $(2g^2 - 5)(2g^2 + 5) =$ 6. $(3g - 2)^2 =$ $x^2 + 4t - 4$ green $x^2 - 4$ red $x^2 + 4$ purple $4g^4 - 25$ lt. pink $4g^4 + 20g - 5$ orange $4g^4 + 25$ lt. yellow $9g^2 - 4$ black $9g^2 - 12g + 4$ dk pink $9g^2 + 4$ orange 7. $b(b^2 - 3b + 4) =$ 8. $(y^2 + y + 2)(y - 2) =$ 9. $3(2x - 1)(3x + 2) =$ $b^3 - 3b^2 + 4$ orange $b^2 - 3b + 4$ red $b^3 - 3b^2 + 4b$ dk. purple $y^3 - y^2 - 4$ pink $y^3 - 2y^2 + 4$ yellow $y^3 - y^2 + 4$ blue $6x^2 - 3x + 12$ pink $18x^2 + 7x - 6$ orange $18x^2 + 3x - 6$ lt. blue 10. $(d - 4)^2$ 11. $(x + 3y)(x - 3y)$ 12. $-d(3 - d) + 2d(d - 1)$ $d^2 - 8d + 16$ dk. red $d^2 - 16$ dk. purple $d^2 + 16$ dk. yellow $x^2 + 9y^2$ dk. blue $x^2 - 9y^2$ dk. pink $x^2 - 6xy - 9y^2$ dk. purple $3d^2 - 3d$ lt. blue $d^2 - 5d$ lt. yellow $3d^2 - 5d$ lt. purple © leslie johnson, 2023 remote learning day 3

Explanation:

Step1: Multiply coefficients & variables

$2xy(3xy) = (2 \times 3)x^{1+1}y^{1+1} = 6x^2y^2$

Step2: Distribute $a$ to each term

$a(a + 3) = a^2 + 3a$

Step3: FOIL the binomials

$(t + 4)(t - 1) = t^2 - t + 4t - 4 = t^2 + 3t - 4$

Step4: Apply difference of squares

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

Step5: Apply difference of squares

$(2g^2 - 5)(2g^2 + 5) = (2g^2)^2 - 5^2 = 4g^4 - 25$

Step6: Square the binomial

$(3g - 2)^2 = (3g)^2 - 2(3g)(2) + 2^2 = 9g^2 - 12g + 4$

Step7: Distribute $b$ to each term

$b(b^2 - 3b + 4) = b^3 - 3b^2 + 4b$

Step8: Distribute trinomial over binomial

$(y^2 + y + 2)(y - 2) = y^3 - 2y^2 + y^2 - 2y + 2y - 4 = y^3 - y^2 - 4$

Step9: FOIL first, then multiply by 3

First: $(2x - 1)(3x + 2) = 6x^2 + 4x - 3x - 2 = 6x^2 + x - 2$
Then: $3(6x^2 + x - 2) = 18x^2 + 3x - 6$

Step10: Square the binomial

$(d - 4)^2 = d^2 - 2(d)(4) + 4^2 = d^2 - 8d + 16$

Step11: Apply difference of squares

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

Step12: Distribute, then combine like terms

First: $-d(3 - d) + 2d(d - 1) = -3d + d^2 + 2d^2 - 2d$
Then: $d^2 + 2d^2 - 3d - 2d = 3d^2 - 5d$

Answer:

1. $6x^2y^2$, Dk. Blue
2. $a^2 + 3a$, Black
3. $t^2 + 3t - 4$, Blue
4. $x^2 - 4$, Red
5. $4g^4 - 25$, Lt. Pink
6. $9g^2 - 12g + 4$, Dk Pink
7. $b^3 - 3b^2 + 4b$, Dk. Purple
8. $y^3 - y^2 - 4$, Pink
9. $18x^2 + 3x - 6$, Lt. Blue
10. $d^2 - 8d + 16$, Dk. Red
11. $x^2 - 9y^2$, Dk. Pink
12. $3d^2 - 5d$, Lt. Purple