Q2. - Algebra 1

Question

State whether each sentence is true or false. If false, replace the underlined phrase or expression to make a true sentence.

$\underset{¯}{\left(x+5\right)\left(x-5\right)}$ is the factorization of a difference of squares.

Step-by-Step Solution

Answer

The given sentence is True.

Step 1. Write the property of difference of Squares.

The property of difference of Squares states that the difference of squares is equal to the product of the sum and difference of the two quantities.

That implies, 

$a^2-b^2=\left(a+b\right)\left(a-b\right)$

Step 2. State whether the given sentence is true or false.

The given expression is $\left(x+5\right)\left(x-5\right)$.

It can be written as:

$\left(x+5\right)\left(x-5\right)=x^2-5^2\left(\because a^2-b^2=\left(a+b\right)\left(a-b\right)\right)$

Therefore, it can be said that the given expression $\left(x+5\right)\left(x-5\right)$ is a factorization of a difference of squares.

Therefore, the given sentence is True.