Question

What is the product of $ 2x + 3 $ and $ 4{x^2} - 5x + 6 $ ?

Answer 1

Hint: Here we are given the one binomial and one trinomial 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 answer:
ake the given expression: $ (2x + 3)(4{x^2} - 5x + 6) $
Now applying the product of terms using the distributive property, the above expression can be written as –
 $ = 2x(4{x^2} - 5x + 6) + 3(4{x^2} - 5x + 6) $
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.
 $ = (2x)(4{x^2}) + (2x)( - 5x) + (2x)(6) + 3(4{x^2}) + 3( - 5x) + 3(6) $
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.
 $ = 8{x^3} - 10{x^2} + 12x + 12{x^2} - 15x + 18 $
Simplify the above expression combining the like terms. Like terms are the terms with the same variable and its power.
 $ = 8{x^3} - \underline {10{x^2} + 12{x^2}} + 1\underline {2x - 15x} + 18 $
Simplify the above expression –
 $ = 8{x^3} + 2{x^2} - 3x + 18 $
This is the required solution.
So, the correct answer is “ $ 8{x^3} + 2{x^2} - 3x + 18 $ ”.

Note: Always remember that the product of one binomial and one trinomial term is always polynomial. Be careful about the sign convention and apply the property of power and exponent while having variables during the product.