Question

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

Answer 1

Hint: In this question, we have been asked to multiply the given terms. To answer this question, use the distributive property of multiplication. Open the first bracket and multiply each term of the first bracket with both the terms of the second bracket. Then, add the like terms and ensure that the terms are written in decreasing order of their powers.

Formula used: Distributive property of multiplication:
$c\left( {a + b} \right) = ac + bc$

Complete step by step answer:
We have been asked to multiply the given terms and find the answer.
$\left( {3x + 4} \right)\left( {2x + 3} \right)$ …. (given)
We will open the first bracket and we will multiply each term of the first bracket with the entire second bracket. See below how it is to be done:
$3x\left( {2x + 3} \right) + 4\left( {2x + 3} \right)$
Next step is to multiply the term written outside the bracket with the term written inside the bracket one-by-one. In this step, the distributive property of multiplication will be used.
$6{x^2} + 9x + 6x + 12$
Now, we will add the like terms and also, ensure that the terms are written in decreasing order of their powers.
$6{x^2} + 15x + 12$
Since the terms are already in their decreasing order of powers, we can leave the answer here.

Hence,$\left( {3x + 4} \right)\left( {2x + 3} \right) = 6{x^2} + 15x + 12$.

Note: What is the distributive property of multiplication?
The distributive property of multiplication says that multiplying two factors $\left( {4 \times 8} \right)$ will result in the same number as multiplying one number $\left( 4 \right)$ with the two numbers $\left( {5 + 3} \right)$ which add up to the second number $\left( 8 \right)$ .
It might sound complicated but let us see what actually happens,
$4 \times 8 = 32$ …. (1)
We can also write $8$ as $5 + 3$ .
$4 \times \left( {5 + 3} \right) = 4 \times 5 + 4 \times 3 = 20 + 12 = 32$ …. (2)
From equation (1) and (2), we know that the distributive property of multiplication is true.