Question

How do you multiply ${{(2x+6)}^{2}}$ ?

Answer 1

Hint: We can write ${{(2x+6)}^{2}}$ in the form $(2x+6)(2x+6)$. Then we use distributive property to get the result. We can directly use ${{(a+b)}^{2}}$ formula to obtain the result as well.

Complete step by step answer:
We can write ${{(2x+6)}^{2}}$ in the form $(2x+6)(2x+6)$.
Distributive property of multiplication says that multiplying the summation of two or more than two addends by a number is the same as multiplying every addend by that number and then adding the products.
According to distributive property if there is an expression in the form $a\times (b+c)$, then we can write this expression in this form $a\times b+a\times c$ as well.
Now using distributive property, we can write the expression- $2x(2x+6)+6(2x+6)$ .
We can see that there are two parts in the above expression. For each one we can use distributive property.
Using distributive property again, we get- \[2x\times 2x+2x\times 6+6\times 2x+6\times 6\] .
Further simplification can be done in the above expression. We can write $2x\times 2x$ equal to $4{{x}^{2}}$ . Then the next two terms are $2x\times 6$ and $6\times 2x$ . You can see both terms are in terms of $x$. Now we can add then and after adding we get $2x\times 6+6\times 2x=12x+12x=24x$. And the last term is ${{6}^{2}}$ which is equal to $36$ .
\[2x\times 2x+2x\times 6+6\times 2x+6\times 6\]
$\Rightarrow 4{{x}^{2}}+12x+12x+36$
$\Rightarrow 4{{x}^{2}}+24x+36$

Hence the multiplication of ${{(2x+6)}^{2}}$ is $4{{x}^{2}}+24x+36$.

Note: We have to use distributive property correctly and should not miss out any term. For squaring and cubing problems, we already have a predefined set of formula which are:
${{\left( a+b \right)}^{2}}={{a}^{2}}+2ab+{{b}^{2}}$ and,
${{\left( a+b \right)}^{3}}={{a}^{3}}+{{b}^{3}}+3ab\left( a+b \right)$