Question

How do you multiply $\left( x-6 \right)\left( x+2 \right)$?

Answer 1

Hint: In this question, we are given two polynomials and we need to multiply them to get a simplified expression in terms of x. For this, we will first multiply every term of one polynomial with every term of the other polynomial taking the signs with terms. After that we will rearrange the terms and add or subtract like terms (if any) to get a simplified expression.

Complete step by step solution:
Here we are given two polynomials which are multiplied as $\left( x-6 \right)\left( x+2 \right)$. We need to simplify the expression in terms of x. For this let us first understand the multiplication of two polynomials. When two polynomials are multiplied every term of one polynomial is multiplied with every term of the other polynomial. Here we have two polynomials having two terms each. So we will get four terms after multiplying each term of one polynomial with each term of another polynomial, we have $\left( x-6 \right)\left( x+2 \right)$.
Let us multiply this by $x\times x-6\times x+2\times x-2\times 6$.
Now let us simplify the terms, for the first term we know that $x\times x$ can be written as ${{x}^{2}}$. For the second term let us write it in the form as -6x. For the third term let us write it in the form as 2x. For last terms we know 2 multiplied by 6 gives 12. So the expression becomes ${{x}^{2}}-6x+2x-12$.
As we can see we can further simplify it by subtracting the like terms 6x and 2x. Here the negative sign is with 6 which is greater so we have -6x+2x = -4x. Hence our expression reduces to ${{x}^{2}}-4x-12$.
This is the final expression as it cannot be simplified further. Therefore, on multiplying $\left( x-6 \right)\left( x+2 \right)$ we get the expression as ${{x}^{2}}-4x-12$.

Note: Students should take care of the signs while multiplying all the terms. For example, while multiplying the terms with -6, take care of negative signs as well. Make sure to multiply each term of one polynomial by each term of the other polynomial.