Question

Expand and combine like terms (3z^5 +7z^2)^2

Answer 1

`\displaystyle{(3z^5+7z^2)^2 = 9z^(10)+42z^7 + 49z^4 }`

Explanation:

Since it's a perfect square, we can simply use the formula:

`\displaystyle{(ax+by)^2 = a^2x^2+2abxy+b^2y^2}`

Given the perfect square expression
`\displaystyle{(3z^5+7z^2)^2}`. Apply perfect square formula:

`\displaystyle{(3z^5+7z^2)^2 = 3^2(z^5)^2+2(3)(7)(z^5)(z^2) + 7^2(z^2)^2 }`

Knowing laws of exponent is mandatory when it comes to algebra. Recall that:

`\displaystyle{(a^m)^n = a^(mn)}\\\\\displaystyle{a^m \cdot a^n = a^(m+n)}`

Apply laws of exponent to simplify the terms or expression:

`\displaystyle{(3z^5+7z^2)^2 = 9z^(10)+42z^7 + 49z^4 }`

Since there are no like-terms to do operation with (these terms have different degrees so they are not considered to be like-terms.) Therefore, the final answer is:

`\displaystyle{(3z^5+7z^2)^2 = 9z^(10)+42z^7 + 49z^4 }`