Question

factor the polynomial by grouping. $4x^2 - 4x + 4x - 25$

Explanation:

Step1: Combine like terms

First, we notice that \(-4x\) and \(+4x\) are like terms. So we combine them:
\(4x^{2}-4x + 4x-25=4x^{2}+( - 4x + 4x)-25\)
\(-4x + 4x = 0\), so the polynomial simplifies to \(4x^{2}-25\)

Step2: Factor the difference of squares

The expression \(4x^{2}-25\) is a difference of squares, since \(4x^{2}=(2x)^{2}\) and \(25 = 5^{2}\). The formula for factoring a difference of squares is \(a^{2}-b^{2}=(a + b)(a - b)\). Here, \(a = 2x\) and \(b = 5\). So we factor it as:
\(4x^{2}-25=(2x + 5)(2x - 5)\)

Answer:

\((2x + 5)(2x - 5)\)