Question

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

Answer 1

Answer:

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

Step-by-step 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:

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