Question

(9x² - 36)(x - 6)

Explanation:

Step1: Factor out 9 from the first binomial

First, we can factor out a common factor of 9 from the expression \(9x^2 - 36\). Using the distributive property \(ab - ac=a(b - c)\), where \(a = 9\), \(b=x^2\) and \(c = 4\) (since \(36\div9 = 4\)), we get:
\(9x^2-36=9(x^2 - 4)\)

Step2: Factor the difference of squares

The expression \(x^2-4\) is a difference of squares, which can be factored using the formula \(a^2 - b^2=(a + b)(a - b)\). Here, \(a=x\) and \(b = 2\) (since \(2^2=4\)), so:
\(x^2-4=(x + 2)(x - 2)\)

Step3: Substitute back and write the final factored form

Substituting \(x^2-4=(x + 2)(x - 2)\) back into \(9(x^2 - 4)\), we have \(9(x + 2)(x - 2)\). Then the original expression \((9x^2-36)(x - 6)\) becomes:
\(9(x + 2)(x - 2)(x - 6)\)

Answer:

\(9(x + 2)(x - 2)(x - 6)\)