Question

How do you multiply $(3x - 2)(3x + 2)?$

Answer 1

Hint: The given expression can be directly multiplied with the help of an algebraic identity, that says the difference of two square terms is equal to the product of addition and subtraction of the terms.

Formula used:
Algebraic identity for difference of square of two terms: ${a^2} - {b^2} = (a + b)(a - b)$

Complete step by step answer:
To multiply the multiplicands $(3x - 2)\;{\text{and}}\;(3x + 2)$, see the multiplicands vigilantly, you will get that both the terms are similar to the terms of an algebraic identity that is the product of sum and difference of two terms is equals to the difference of square of the terms, that is mathematically given as follows
${a^2} - {b^2} = (a + b)(a - b)$

On comparing the expression $(a + b)(a - b)$ and the given expression $(3x - 2)(3x + 2)$, we get
$a = 3x\;{\text{and}}\;b = 2$
So putting it above to find the value of required multiplication, we will get
$(3x - 2)(3x + 2) = (3x + 2)(3x - 2) \\
\Rightarrow(3x - 2)(3x + 2)= {(3x)^2} - {2^2} \\
\therefore(3x - 2)(3x + 2)= 9{x^2} - 4 \\ $
Therefore $9{x^2} - 4$ is the result of the multiplication of $(3x - 2)\;{\text{and}}\;(3x + 2)$.

Note:We have written $(3x - 2)(3x + 2) = (3x + 2)(3x - 2)$ with the help of commutative property of multiplication, which says in multiplication order of multiplicands, does not affects the result of multiplication. Multiplicand is a term which is to be multiplied with another multiplicand. Terms in this problem has been multiplied directly with the help of the algebraic identity but circumstances are different for each question out there, so here is a general tip to solve this type of questions, first consider one of the factors in the multiplication to be constant and then use the distributive property of the multiplication to multiply the terms accordingly and multiply the terms after removing the brackets.