Question

How do you multiply the expression $4x - 3\left( {2 - x} \right)$?

Answer 1

Hint: In this question we are asked to multiply the two terms and then simplify the expression, this can be done by using the FOIL method and the Foil method is a technique used to help remember the steps required to multiply two binomials. Multiply each term in the first binomial with each term in the second binomial using Foil method as shown,
\[\left( {ax + b} \right)\left( {cx + d} \right) = ax \cdot cx + ax \cdot d + b \cdot cx + b \cdot d\].
Now substituting the values and multiplying each term and then subtracting the like terms, we will get the required result.

Complete step-by-step solution:
Given expression is $4x - 3\left( {2 - x} \right)$,
Take the second part of the expression, i.e.,$3\left( {2 - x} \right)$,
Multiply the constant with the first term in the binomial that are \[2\] from $2 - x$ and \[3\]. The product of \[2\] and \[3\] i.e.,
$ \Rightarrow $\[2 \cdot 3 = 6\],
Now then we will multiply the constant term with the second term of the binomial, the product of outer terms that are \[x\] from \[2 - x\] and 3 i.e.,
$ \Rightarrow $\[3 \cdot - x = - 3x\],
So this is can represented as,
$ \Rightarrow 3\left( {2 - x} \right) = 6 - 3x$,
Now subtracting the second term from the first term, we get,
$ \Rightarrow 4x - 6 - \left( { - 3x} \right)$,
By simplifying we get,
\[ \Rightarrow 4x - 6 + 3x\],
Now adding the like terms we get,
$ \Rightarrow 7x - 6$,
So, the required answer is $7x - 6$.

By multiplying the terms in the given question $4x - 3\left( {2 - x} \right)$ we get,
$4x - 3\left( {2 - x} \right) = 7x - 6$.

Note: Steps of foil method will be: First multiply the first terms, then the outer terms, then the inner terms and finally the last terms.
The product of two positive will be positive.
The product of two negatives will also be positive.
The product of a positive and negative will always be negative.