Question

rewrite without parentheses.
$-9y^{6}(-8y^{2}+7)$
simplify your answer as much as possible.

Explanation:

Step1: Apply distributive property

We use the distributive property \(a(b + c)=ab+ac\). Here, \(a = - 9y^{6}\), \(b=-8y^{2}\), and \(c = 7\). So we have:
\(-9y^{6}\times(-8y^{2})+(-9y^{6})\times7\)

Step2: Multiply coefficients and add exponents for \(y\)

For the first term, multiply the coefficients \(-9\times(-8) = 72\), and add the exponents of \(y\) (using the rule \(y^{m}\times y^{n}=y^{m + n}\)): \(y^{6}\times y^{2}=y^{6 + 2}=y^{8}\). So the first term is \(72y^{8}\).
For the second term, multiply \(-9\times7=-63\), and the variable part remains \(y^{6}\). So the second term is \(-63y^{6}\).

Answer:

\(72y^{8}-63y^{6}\)