Question

1. Match the polynomial identity to the correct answer.

Answer 1

Answer:

$a: (a-b)(a+b);b: (a-b)(a^{2}+ab+b^{2}); c: (a^{2} +2ab+b^{2}); d: (a+b)(a^{2}- ab+b^{2})$

Step-by-step explanation:

Given the expressions all that is required is to expand them (using the distributive property) to see which answers they match up to:

For a: $(a-b)(a+b)=a^{2} +ab-ab-b^{2} =a^{2}-b^2$

For b: $(a-b)(a^2+ab+b^2)=a^3+a^2b+ab^2-a^2b-ab^2-b^3=a^3-b^3$

For c calculate the square of a sum: $(a+b)^2=a^2+ab+ab+b^2$

(add like terms) c: $a^2+2ab+b^2$

For d: $(a+b)(a^2-ab+b^2)=a^3-a^2b+ab^2+a^2b-ab^2+b^3$$=a^3+b^3$