Question

How do you multiply $(x + 3)(x - 7)?$

Answer 1

Hint: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. You have to use the distributive property twice in this multiplication.Distributive property of multiplication is given as following: $a(b + c) = ab + ac$

Complete step by step answer:
 In order to multiply the terms $(x + 3)\;{\text{and}}\;(x - 7)$ we will consider $(x - 7)$ being constant and use the distributive property of multiplication as follows:
$
(x + 3)(x - 7) \\
\Rightarrow x(x - 7) + 3(x - 7) \\ $
Now again we will use the distributive property of multiplication here to multiply the terms further
$
x(x - 7) + 3(x - 7) \\
\Rightarrow(x \times x - 7x) + (3x - 3 \times 7) \\
\Rightarrow(x \times x - 7x) + (3x - 21) \\ $
Now from the law of indices for multiplication, we know that if multiplicands have similar or equal bases then their powers or exponents are being added. Let us understand this law of indices with help of a general example, a number “a” with power “b” is being multiplied to a number “a” with power “c”, we can see here the base of multiplicands are equal, that is “a”, then their product is given as “a” to the power “b” plus “c”, mathematically it can be given as follows${a^b} \times {a^c} = {a^{b + c}}$.

With help of this law of indices, we can further write the above expression as,
$
(x \times x - 7x) + (3x - 21) \\
\Rightarrow({x^{1 + 1}} - 7x) + (3x - 21) \\
\Rightarrow({x^2} - 7x) + (3x - 21) \\ $
Now grouping the similar terms, that is terms of ${x^2},\;x$ and constant respectively, we will get
$
{x^2} - (7x + 3x) - 21 \\
\therefore {x^2} - 4x - 21 \\
 $
Therefore ${x^2} - 4x - 21$ is the result of the multiplication of $(x + 3)\;{\text{and}}\;(x - 7)$

Note:Multiplicands are the terms which are to be multiplied by other multiplicands.On multiplication of this type of variable terms, take care of the signs and also make sure you have simplified the similar terms after the multiplication.