Question

1. 8w^7(8w + 7w^4) 14) 7x(3x^3 - 5x^2+2x - 6) 15) - 6x(4x - 3) 16) - 7x(3x^4) 17) - 6(k^2 - 2) 18) x(6x^2+4x - 1) 19) find the area of each rectangle below. write your answer in standard form. classification: 20) classification: 21) classification:

Explanation:

13)

Step1: Use distributive property

$8w^{7}(8w + 7w^{4})=8w^{7}\times8w+8w^{7}\times7w^{4}$

Step2: Apply exponent - rule $a^{m}\cdot a^{n}=a^{m + n}$

$8w^{7}\times8w=(8\times8)w^{7 + 1}=64w^{8}$ and $8w^{7}\times7w^{4}=(8\times7)w^{7+4}=56w^{11}$

Step3: Combine terms

$64w^{8}+56w^{11}$

Step1: Use distributive property

$7x(3x^{3}-5x^{2}+2x - 6)=7x\times3x^{3}-7x\times5x^{2}+7x\times2x-7x\times6$

Step2: Apply exponent - rule $a^{m}\cdot a^{n}=a^{m + n}$

$7x\times3x^{3}=(7\times3)x^{1 + 3}=21x^{4}$, $7x\times5x^{2}=(7\times5)x^{1+2}=35x^{3}$, $7x\times2x=(7\times2)x^{1 + 1}=14x^{2}$, $7x\times6 = 42x$

Step3: Combine terms

$21x^{4}-35x^{3}+14x^{2}-42x$

Step1: Use distributive property

$-6x(4x - 3)=-6x\times4x+(-6x)\times(-3)$

Step2: Apply exponent - rule $a^{m}\cdot a^{n}=a^{m + n}$

$-6x\times4x=(-6\times4)x^{1+1}=-24x^{2}$ and $(-6x)\times(-3)=18x$

Step3: Combine terms

$-24x^{2}+18x$

Answer:

$56w^{11}+64w^{8}$

14)