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webwork / hs rowe cpma / 5.5 multiplying polynomials / 11
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5.5 multiplying polynomials: problem 11
(1 point)
the expression $(3x - 9)(3x + 9)$ equals $\square x^{2}-\square$
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Explanation:

Step1: Use the difference of squares formula

The formula \((a - b)(a + b)=a^{2}-b^{2}\). Here \(a = 3x\) and \(b = 9\).
So \((3x-9)(3x + 9)=(3x)^{2}-9^{2}\).

Step2: Calculate \((3x)^{2}\) and \(9^{2}\)

For \((3x)^{2}\), using the power - of - a - product rule \((ab)^{n}=a^{n}b^{n}\), we have \((3x)^{2}=3^{2}\times x^{2}=9x^{2}\).
For \(9^{2}\), \(9^{2}=81\).

Answer:

\(9x^{2}-81\)