Question

How do you multiply \[\left( {w + 3} \right)\left( {4w - 4} \right)\] ?

Answer 1

Hint: We have an algebraic expression and we need to simplify this. Here we have ‘4w’ and ‘w’ 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. We have the product of two monomials.

Complete step by step solution:
Given,
 \[\left( {w + 3} \right)\left( {4w - 4} \right)\]
Here we multiply ‘w’ with \[\left( {4w - 4} \right)\] and multiply 3 with \[\left( {4w - 4} \right)\] .
 \[ \Rightarrow w\left( {4w - 4} \right) + 3\left( {4w - 4} \right)\]
 \[ \Rightarrow \left( {4{w^2} - 4w} \right) + \left( {12w - 12} \right)\]
 \[ \Rightarrow 4{w^2} - 4w + 12w - 12\]
Adding like terms we have,
 \[ \Rightarrow 4{w^2} + 8w - 12\]
Hence the multiplication of \[\left( {w + 3} \right)\left( {4w - 4} \right)\] is \[ \Rightarrow 4{w^2} + 8w - 12\] .
So, the correct answer is “ \[ 4{w^2} + 8w - 12\] .”.

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.
Here we have a polynomial of degree 2 and it is called a quadratic equation. We can solve this using factorization method or quadratic equations. We use this formula for multiplying, that is \[\left( {a + b} \right)\left( {c + d} \right) = ac + ad + bc + bd\] . In fact the given problem \[\left( {w + 3} \right)\left( {4w - 4} \right)\] are the factors of the quadratic equation \[4{w^2} + 8w - 12\] .