Question

How do you simplify $\left( x+8 \right)\left( {{x}^{2}}-7x-3 \right)$ ?

Answer 1

Hint: In this question, we have to simplify the given algebraic term. Thus, we will use the distributive property and the basic mathematical rules to get the solution. As we know, the distributive property is the opening of the brackets that is multiplying the number with another number and then adding the products together. So, firstly, we will apply the distributive property $\left( a+b \right)\left( c-d-e \right)=ac-ad-ae+bc-bd-be$ in the given algebraic term. Then, we will make the necessary calculations by applying the basic mathematical rules, to get the required result for the solution.

Complete step by step solution:
According to the question, we have to simplify the given algebraic term.
The distributive property means multiplying the number with each number and then adding the products together. Thus, we will apply the distributive property to get the solution.
The algebraic term given to us is $\left( x+8 \right)\left( {{x}^{2}}-7x-3 \right)$ ----------- (1)
First, we will use the distributive property $\left( a+b \right)\left( c-d-e \right)=ac-ad-ae+bc-bd-be$ term (1), we get
$x\left( {{x}^{2}} \right)+x\left( -7x \right)+x\left( -3 \right)+8\left( {{x}^{2}} \right)+8\left( -7x \right)+8\left( -3 \right)$
Now, we will open the brackets of the above term for further simplification, we get
${{x}^{3}}-7{{x}^{2}}-3x+8{{x}^{2}}-56x-24$
Now, we will solve the same variables of the above term, we get
${{x}^{3}}+{{x}^{2}}-59x-24$
Thus, we cannot solve the above equation furthermore.

Therefore, for the algebraic term $\left( x+8 \right)\left( {{x}^{2}}-7x-3 \right)$ , its simplified value is ${{x}^{3}}+{{x}^{2}}-59x-24$ which is the required solution.

Note: While solving this problem, keep in mind the formula you are using and mention it properly to avoid confusion and mathematical error. After applying the distributive property, when you open the brackets, do not forget to put the negative sign wherever it is applicable to get an accurate answer.