Question

Factor completely, then place the answer in the proper location on the grid. a3 - b3

Answer 1

`\bf \textit{difference of cubes} \\\\ a^3+b^3 = (a+b)(a^2-ab+b^2)\qquad (a+b)(a^2-ab+b^2)= a^3+b^3 \\\\ a^3-b^3 = (a-b)(a^2+ab+b^2)\qquad (a-b)(a^2+ab+b^2)= a^3-b^3\\\\ -------------------------------\\\\ a^3-b^3\implies (a-b)(a^2+ab+b^2)`

Answer 2

We have to find the difference of cubes of any two real numbers

`a^3-b^3=(a-b)(a^2+ab+b^2)`

Verification of the Result

RHS

`=(a-b)(a^2+ab+b^2)\\\\=a * (a^2+ab+b^2)-b * (a^2+ab+b^2)\\\\\text{Using Distributive property }\\\\=a^3+a^2b+ab^2-ba^2-ab^2-b^3\\\\ \text{Cancelling like terms}\\\\=a^3-b^3`

=LHS