Question

How do you simplify $\left( {x + 3} \right)\left( {2x + 7} \right)?$

Answer 1

Hint: In this question, we are going to simplify the given equation.
First we are going to expand the given equation by applying the distributive property.
Next simplify and combine like terms, we get the required result.
We can also find the values of $x$ from the given equation.
Property used:
The distributive property of multiplication states that
$a\left( {b + c} \right) = ab + ac$

Complete step-by-step solution:
In this question, we are going to simplify the equation and find the value of $x$ from the given equation.
First we are going to expand the given term $\left( {x + 3} \right)\left( {2x + 7} \right)$ by FOIL method.
Now we are going to apply the distributive property to the given equation,
$ \Rightarrow x\left( {2x + 7} \right) + 3\left( {2x + 7} \right)$
$ \Rightarrow x \times 2x + x \times 7 + 3 \times 2x + 3 \times 7$
Now we are going to simplify and combine the like terms
Multiply each term we get,
$ \Rightarrow 2{x^2} + 7x + 6x + 21$
Adding the two middle terms, we get
$ \Rightarrow 2{x^2} + 13x + 21$
Hence we get the required solution.
$ \Rightarrow \left( {x + 3} \right)\left( {2x + 7} \right)$
Now we are going to equate this equal to zero.
$ \Rightarrow \left( {x + 3} \right)\left( {2x + 7} \right) = 0$
$ \Rightarrow \left( {x + 3} \right) = 0,\left( {2x + 7} \right) = 0$
$ \Rightarrow x = - 3,2x = - 7$
$ \Rightarrow x = - 3,x = \dfrac{{ - 7}}{2}$
$ \Rightarrow x = - 3,\dfrac{{ - 7}}{2}$

Therefore the value of x is equal to -3 and $\dfrac{{ - 7}}{2}$.

Note: To distribute means divide something or give a share or part of something.
According to the distributive property, multiplying the sum of two or more addends by a number will give the same result as multiplying each addend individually by the number and then adding the products together.
The distributive property helps in making difficult problems simpler.
FOIL method is nothing but a technique for distributing two binomials. The letters FOIL stand for First, Outer, Inner, Last. First means multiply the terms which occur first in each binomial, Outer means multiply the outermost terms in the product, Inner means multiply the innermost terms, and Last means multiply the terms which occur last in each binomial.