Question

Which of the following is equivalent to (2x + 3)(2x + 3)?

Answer 1

The correct answer is option C. 4x² + 12x + 9

Explanation:

Identity

(a + b )² = a²+ 2ab + b²

It is given that

(2x + 3)(2x + 3) = (2x + 3)²

Here a = 2x and b = 3

Therefore

(2x + 3 )² = (2x)² + 2*2x*3 + 3²

(2x + 3 )² = 4x² + 12x + 9

Therfore the correct optin is Option C). 4x² + 12x + 9

Answer 2

The product of two equal values ​​can be expressed by one of these squared values. For example,

`\mathsf{(2x+3)(2x+3)=(2x+3)^2}`

The sum of two terms squared can be solved by a remarkable product called "square of the sum of two terms", which is expressed as follows:

• 
  `\mathsf{(a+b)^2=a^2+2ab+b^2}`

Developing, changing the values, we will have:

`\begin{array}{rl} \mathsf{(2x+3)^2}&\mathsf{=(2x)^2+2(2x)(3)+3^2}\\\\ &\mathsf{=4x^2+4x(3)+9}\\\\ \underline{&\mathsf{=4x^2+12x+9}} \end{array}`

The answer is C.

_____

The development of remarkable products is done as follows:

`\begin{array}{rl} \mathsf{(a+b)^2}&\mathsf{=(a+b)\cdot(a+b)}\\\\ &\mathsf{=a^2+ab+ab+b^2}\\\\ &\mathsf{=a^2+2ab+b^2}\end{array}`