Question

How do you find the product $ (4x + 5)(4x + 5)? $

Answer 1

Hint: Here we are given the two binomial terms to find the product of it. Binomial terms are the polynomial equation with two terms which are usually joined with the plus or minus sign. Will apply the product properties and find the resultant value.

Complete step by step solution:
Take the given expression: $ (4x + 5)(4x + 5) $
Now applying the product of two binomials, the above expression can be written as –
 $ = 4x(4x + 5) + 5(4x + 5) $
Simplify the above expression finding the product of the terms inside the bracket. When there is a positive term outside the bracket then the sign of the terms inside the brackets changes when opened.
 $ = 4x(4x) + 4x(5) + 5(4x) + 5(5) $
Simplify the above expression by using the property of power and exponent which states that when bases are the same then the powers are added.
 $ = 16{x^2} + 20x + 20x + 25 $
Simplify the above expression combining the like terms. Like terms are the terms with the same variable and its power.
 $ = 16{x^2} + \underline {20x + 20x} + 25 $
Simplify the above expression –
 $ = 16{x^2} + 40x + 25 $
This is the required solution.
So, the correct answer is “$16{x^2} + 40x + 25 $”.

Note: The power is used to express mathematical equations in the short form; it is an expression that represents the repeated multiplication of the same factor. For example - $ 2 \times 2 \times 2 $ can be expressed as $ {2^3} $ . Here, the number two is called the base and the exponent represents the number of times the base is used as the factor.