Factor. \[ 36 y^{2}-49 \]

To factor the expression $$ 36y^{2} - 49 $$, we can recognize it as a **difference of squares**. The difference of squares formula is: \[ a^{2} - b^{2} = (a - b)(a + b) \] Let's apply this to the given expression: 1. **Identify $$ a $$ and $$ b $$:** \[ 36y^{2} = (6y)^{2} \quad \text{and} \quad 49 = 7^{2} \] So, $$ a = 6y $$ and $$ b = 7 $$. 2. **Apply the difference of squares formula:** \[ 36y^{2} - 49 = (6y)^{2} - 7^{2} = (6y - 7)(6y + 7) \] **Final Factored Form:** \[ 36y^{2} - 49 = (6y - 7)(6y + 7) \] The expression $$ 36y^{2} - 49 $$ factors to $$ (6y - 7)(6y + 7) $$.

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Premium

Home Question Bank Math Algebra

Question

Factor.

Ask by King Bowen. in the United States

Jan 27,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

The expression

factors to

Solution

To factor the expression

, we can recognize it as a difference of squares. The difference of squares formula is:

Let’s apply this to the given expression:

Identify and :

So, and .
Apply the difference of squares formula:

Final Factored Form:

Answered by UpStudy AI and reviewed by a Professional Tutor

error msg

Explain

Simplify this solution

Bonus Knowledge

To factor the expression

, you can recognize it as a difference of squares. Recall that a difference of squares can be factored using the formula:

Here,

and

. So we can rewrite the expression as:

Applying the difference of squares formula gives:

So, the factored form of the expression

is:

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