Question

How do you multiply \[4\left( {3x + 5} \right) - 2\left( {5x - 1} \right)\] ?

Answer 1

Hint: We have an algebraic expression and we need to simplify this. Here we have ‘3x’ and ‘5x’ 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 3x meaning that 3 is a coefficient of ‘x’ and 5x means 5 is a coefficient of x.

Complete step by step solution:
Given,
 \[4\left( {3x + 5} \right) - 2\left( {5x - 1} \right)\]
That is,
 \[ \Rightarrow 4 \times \left( {3x + 5} \right) - 2 \times \left( {5x - 1} \right)\]
Now multiplying the numbers inside the brackets for each terms
 \[ \Rightarrow \left( {12x + 20} \right) - \left( {10x - 2} \right)\]
 \[ \Rightarrow 12x + 20 - 10x + 2\]
Adding the like terms and constants we have,
 \[ \Rightarrow 2x + 22\]
Hence the multiplication of \[4\left( {3x + 5} \right) - 2\left( {5x - 1} \right)\] is
 \[ \Rightarrow 2x + 22\] .
 \[ \Rightarrow 2(x + 11)\]
So, the correct answer is “2(x + 11)”.

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.
We know the product of a negative number and a negative number results in a positive number. Similarly the product of a negative (positive) number and a positive (negative) number results in a negative number.