Question

How do you use the distributive property when you multiply polynomials?

Answer 1

Hint: From the given question we are asked to find that how is the distributive property used in the multiplication of polynomials. For solving this question we will explain the process of distributive property in multiplying the polynomials along with it. We will take the help of an example and make the solution brief. So, we proceed with the solution as follows.

Complete step by step solution:
When multiplying the polynomials (more than one monomial), the basic property in mathematics which is distributive property allows us to multiply each term of the first polynomial by each term of the second.
We after doing the above process then add the products we got together and combine the like terms and simplify further using basic mathematical operations like addition and subtraction.
For example we will multiply the polynomial $\Rightarrow \left( 2x+1 \right)(x+4)$ using the distributive property.
$\Rightarrow \left( 2x+1 \right)(x+4)$
Now we will take the terms $2x$ and $1$ of the first polynomial and multiply with each term of the second polynomial.
So, we get,
$\Rightarrow 2x(x+4)+1(x+4)$
So, the products we will get are as follows.
$\Rightarrow 2{{x}^{2}}+8x+x+4$
Now we will add the like terms $8x$ and $x$. So, we get the expression reduced as follows.
$\Rightarrow 2{{x}^{2}}+9x+4$
Therefore, in this way we will multiply polynomials using the distributive property.

Note: Students should be very careful in doing the calculations. The given example is done for binomials. In the same way we can do it for monomials. For example, $\Rightarrow 2\left( x+4 \right)$ we will multiply the term $2$ with the both terms of the second polynomial. We get, $\Rightarrow 2(x)+2(4)$
$\Rightarrow 2x+8$