Question

The area of a square is equal to the expression $(4x^2+6x+6x+9)sq$ units. Find an algebraic expression for the length of the side of the square.

• A. $(2x+3)$
• B. $(2x+2)$
• C. $(x+3)$
• D. None of these

Answer 1

The correct option is A $(2x+3)$

4x²+12x+9= 4x²+12x+9

We find two numbers that multiply to get 36, but add to get 12.

These terms are, 6 and 6

6 × 6 =36

6 + 6 =12

So, we use these terms and replace them with 12x

4x²+6x+6x+9

We factor out the first two terms

4x² =2 ×2 × x ×x

6x=2 ×3 ×x

We can see that they both share a factor of 2x

So, we write it as 2x(2x+3)

Now, we factor out the next two terms.

6x=2 ×3 ×x

9=3 ×3

We can see that these two have a common factor of 3

So, we write it as 3(2x+3)

We put the two together 2x(2x+3)+3(2x+3)

We add them, and get (2x+3)(2x+3)

In other words, the length is 2x+3