Question

How do you multiply \[4a(5a - 2)\] ?

Answer 1

Hint: We have an algebraic expression and we need to simplify this. Here we have ‘4a’ and ‘5a’ are algebraic terms. The multiplication of two or more monomial expressions or expressions with one term means finding the product of all the expressions involved. Here we have 4a meaning that 4 is a coefficient of ‘a’ and 5a means 5 is a coefficient of a.

Complete step by step solution:
Given,
 \[4a(5a - 2)\]
That is,
 \[ \Rightarrow 4a \times (5a - 2)\]
Now applying the multiplying ‘4a’ with each of the terms in brackets.
 \[ \Rightarrow (4a \times 5a) - (4a \times 2)\]
 \[ \Rightarrow \left( {\left( {(4 \times 5)(a \times a)} \right) - ((4 \times 2)a)} \right)\]
All we did is multiply the coefficients and the variables separately. Here ‘a’ is the variable or unknown term.
 \[ \Rightarrow \left( {\left( {20{a^2}} \right) - \left( {8a} \right)} \right)\]
 \[ \Rightarrow 20{a^2} - 8a\] .
Hence the multiplication of \[4a(5a - 2)\] is \[ \Rightarrow 20{a^2} - 8a\] .
So, the correct answer is “ \[ 20{a^2} - 8a\] ”.

Note: If we the value of ‘a’ we will have a value for the given expression. While multiplication of monomials by monomial expression the rule or equation that applies is product of their coefficients and product of the variables. The rule that applies to the multiplication of monomials and a polynomial is the distributive law. The law shows that each term of the polynomial should be individually multiplied by the monomial expression.