QuestionFactor the expressions: $6 x^{2}+48 x$ and $x^{2}-49$ .

Studdy Solution

STEP 1

Assumptions1. We are given two expressions $6x^{}+48x$ and $x^{}-49$ . We need to factorize these expressions

STEP 2

Let's start with the first expression $6x^{2}+48x$ . We need to find the greatest common factor (GCF) of the terms in the expression.

STEP 3

The GCF of $6x^{2}$ and $48x$ is $6x$ .

STEP 4

Factor out the GCF from the expression.
$6x^{2}+48x =6x(x+8)$

STEP 5

Now, let's move on to the second expression $x^{2}-49$ . This is a difference of squares, which can be factored using the formula $a^{2}-b^{2} = (a-b)(a+b)$ .

STEP 6

Identify the squares in the expression. Here, $a^{2} = x^{2}$ and $b^{2} =49$ .

STEP 7

Take the square root of $a^{2}$ and $b^{2}$ to find the values of $a$ and $b$ . Here, $a = x$ and $b =7$ .

STEP 8

Substitute the values of $a$ and $b$ into the formula to factorize the expression.
$x^{2}-49 = (x-7)(x+7)$ So, the factorized forms of the given expressions are $6x(x+8)$ and $(x-7)(x+7)$ .

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