To find the product of [tex]\((2x + 4)(2x - 2)\)[/tex], we need to use the distributive property, also known as FOIL (First, Outer, Inner, Last) method. Here are the steps broken down in detail:
1. First: Multiply the first terms in each binomial:
[tex]\[
(2x) \cdot (2x) = 4x^2
\][/tex]
2. Outer: Multiply the outer terms in each binomial:
[tex]\[
(2x) \cdot (-2) = -4x
\][/tex]
3. Inner: Multiply the inner terms in each binomial:
[tex]\[
4 \cdot (2x) = 8x
\][/tex]
4. Last: Multiply the last terms in each binomial:
[tex]\[
4 \cdot (-2) = -8
\][/tex]
Now, we need to combine all these results:
[tex]\[
4x^2 - 4x + 8x - 8
\][/tex]
Next, we combine the like terms [tex]\(-4x\)[/tex] and [tex]\(8x\)[/tex]:
[tex]\[
4x^2 + 4x - 8
\][/tex]
Therefore, the expanded form of [tex]\((2x + 4)(2x - 2)\)[/tex] is:
[tex]\[
4x^2 + 4x - 8
\][/tex]
