Question

How do you multiply $\left( x+y \right)\left( x+y \right)$?

Answer 1

Hint: To get the solution for the given question, we have to use the distributive property. After applying that distributive property, we need to combine the terms with the proper signs then simplification should be done for each term to get the final answer. The following property is used for solving the solution:

Complete step by step answer:
According to the given question, we have been asked to multiply the factors $\left( x+y \right)\left( x+y \right)$.
To start with this question, we should know about distributive property, that is $c\times \left( a+b \right)=a\times c+b\times c$
So, to multiply the given factors we are now applying the distributive property,
\[\Rightarrow x\times \left( x+y \right)+\left( x+y \right)\times y\]
Again, applying the distributive property for the first term, we get
\[\Rightarrow x\times x+x\times y+\left( x+y \right)\times y\]
Now applying the distributive property for the second term, we get
$\Rightarrow x\times x+x\times y+x\times y+y\times y$
We know that the power rule states that ${{a}^{m}}\times {{a}^{n}}={{a}^{m+n}}$
Applying the power rule for the equation we get $x\times x={{x}^{1}}\times {{x}^{1}}={{x}^{2}}$ and in the same way $y\times y={{y}^{1}}\times {{y}^{1}}={{y}^{2}}$
$\Rightarrow {{x}^{2}}+xy+xy+{{y}^{2}}$
To simplify the terms, the coefficient of the like terms should be added and if there is no coefficient for the variable then we should write the variable with 1 as the coefficient. So, we can write
$\Rightarrow {{x}^{2}}+1xy+1xy+{{y}^{2}}$
Now, adding the coefficient of term $xy$, which gives
$\Rightarrow {{x}^{2}}+\left( 1+1 \right)xy+{{y}^{2}}$
$\Rightarrow {{x}^{2}}+2xy+{{y}^{2}}$ which is the multiplication of given factors.

$\therefore {{x}^{2}}+2xy+{{y}^{2}}$ is the required answer.

Note: In case, if we have a negative sign multiply it properly with another variable otherwise the result will be wrong. While multiplying using distributive property check whether every term is multiplied with the other term correctly. While multiplying the terms which involve two or more operations then the BODMAS rule should be used. Also, we can learn this as an identity for further uses.