The expression given is 16x² − 144. We need to factor this expression. Step 1: Find the greatest common factor (GCF) of the terms. The terms are 16x² and 144. The GCF of 16 and 144 is 16. 16x² − 144 = 16(x² − 9) Step 2: Factor the expression inside the parentheses. The expression x² − 9 is a difference of squares, which follows the form a² − b² = (a−b)(a+b). Here, a² = x² ⇒ a = x and b² = 9 ⇒ b = 3. So, x² − 9 = (x − 3)(x + 3). Step 3: Combine the factors. Substitute the factored form of x² − 9 back into the expression from Step 1. 16(x² − 9) = 16(x − 3)(x + 3) The completely factored form of the expression is: 16(x − 3)(x + 3)

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16x2 - 144

June 2, 2026Mathematics

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Answer

16(x - 3)(x + 3)

Step-by-step solution

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The expression given is $16x^2 - 144$ . We need to factor this expression.

Find the greatest common factor (GCF) of the terms.
The terms are $16x^2$ and 144.
The GCF of 16 and 144 is 16.
$16x^2 - 144 = 16(x^2 - 9)$
Factor the expression inside the parentheses.
The expression $x^2 - 9$ is a difference of squares, which follows the form $a^2 - b^2 = (a-b)(a+b)$ .
Here, $a^2 = x^2 \implies a = x$ and $b^2 = 9 \implies b = 3$ .
So, $x^2 - 9 = (x - 3)(x + 3)$ .
Combine the factors.
Substitute the factored form of $x^2 - 9$ back into the expression from Step 1.
$16(x^2 - 9) = 16(x - 3)(x + 3)$
The completely factored form of the expression is:
$16(x - 3)(x + 3)$

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16x2 - 144

Answer

Step-by-step solution

Find the greatest common factor (GCF) of the terms.

Factor the expression inside the parentheses.

Combine the factors.

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