Question

I need help with my homework

Answer 1

4x² - 36

Explanation:

To find the product of the expression (2x - 6)(2x + 6), we can use the method of "FOILing." The FOIL method is a mnemonic used to multiply two binomials (an expression with two terms).

FOIL stands for:

• F - Multiply the First terms of each binomial.

• O - Multiply the Outer terms of each binomial.

• I - Multiply the Inner terms of each binomial.

• L - Multiply the Last terms of each binomial.

`(a+b)(c+d)=ac+ad+bc+bd\\\\\hrule`

Let's break down the multiplication step-by-step:

First, we multiply the first terms of each expression (the "F" in FOIL):

2x · 2x = 4x²

Next, we multiply the outer terms (the "O" in FOIL):

2x · 6 = 12x

Then, we multiply the inner terms (the "I" in FOIL):

-6 · 2x = -12x

Finally, we multiply the last terms (the "L" in FOIL):

-6 · 6 = -36

Now, let's combine the results:

4x² + 12x - 12x - 36

Since the terms 12x and -12x cancel each other out (they have equal magnitude but opposite signs), we are left with:

4x² - 36

Thus, the product of (2x - 6)(2x + 6) is 4x² - 36.