Question

Use a suitable identity to get the following product $(2y + 5)(2y + 5)$
$A)4{y^2} + 20y + 25$
$B)4{y^2} + 10y + 25$
$C)4{y^2} + 20y + 15$
$D)4{y^2} + 20y - 25$

Answer 1

Hint: Here we are asked to find the product of the given algebraic expression. The algebraic expression is nothing but the expression of combination of unknown variables with or without coefficients along with arithmetic operations. These algebraic equations are multiplied term by term. One term from any one of the given expressions is taken and multiplied to all other terms in the other expression and written as a sum along with their signs. This process of multiplying is repeated until all the individual terms in one expression are multiplied with all other terms in the other expression. Then it can be simplified if needed.

Complete step by step solution:
Since the product of the two values means, which is the process of using the multiplication operation only. Hence the multiplication of the $(2y + 5)(2y + 5)$ is the requirement
Let $(2y + 5) \times (2y + 5)$ is the expression of the given question.
Since applying the multiplication we get $(2y + 5)(2y + 5) \Rightarrow (2y \times 2y) + (2y \times 5) + (5 \times 2y) + (5 \times 5)$
Thus, we have $(4{y^2}) + (10y) + (10y) + (25)$
Hence using the addition, we get $(4{y^2}) + (10y) + (10y) + (25) = 4{y^2} + 20y + 25$
Hence product of $(2y + 5)(2y + 5)$ is $4{y^2} + 20y + 25$
Therefore, the option $A)4{y^2} + 20y + 25$ is correct.

So, the correct answer is “Option A”.

Note: In the above problem, we have done multiplication with two algebraic equations if we are supposed to do addition or subtraction, we will do it in the following way:
Addition: $(2y + 5) + (2y + 5) = \left( {2y + 2y} \right) + 5 + 5 = 4y + 10 = 2\left( {2y + 5} \right)$
Subtraction: \[(2y + 5) - (2y + 5) = 2y + 5 - 2y + 5 = \left( {2y - 2y} \right) + 5 + 5 = 10\]
We can see that while doing addition and subtraction we have grouped the terms having the unknown variables and the constants separately those are called like terms. The terms having the same unknown variables are called like terms and terms having different variables are called unlike terms. On simplifying the algebraic expression, we only have to group the like terms we are not allowed to group unlike terms.