Question

How do you simplify the product of \[(a-6)(a+8)\] and write it in standard form?

Answer 1

Hint: to find the product of the given expression we will follow a few steps. First, we will remove the brackets. This means we have to expand the expression. Then simply add the like terms and you will get the equation in \[a{{x}^{2}}+bx+c=0\] form which is the standard form of the equation.

Complete step by step answer:
In the above question, the expression is \[(a-6)(a+8)\] . Our first step is to expand the expression by opening the brackets. In order to expand it, we will multiply the first term of the first expression with the first term of the second expression. Then our second step would be to multiply the first term of the first expression with the second term of the second expression. After that, we will take the second term of the first expression and the first term of the second expression and then multiply with each other. The last step is that we will take the second term of the first expression and the second term of the second expression and then multiply with each other. First, we will multiply the two \[a's\] after that multiply \[a\] with \[8\] . Then we will take the second term \[-6\] with \[a\] and then multiply \[-6\] with \[8\] .
\[\begin{align}
  & (a-6)(a+8) \\
 & \Rightarrow a\times a+a\times 8+(-6\times a)+(-6\times 8) \\
 & \Rightarrow {{a}^{2}}+8a-6a-48 \\
 & \Rightarrow {{a}^{2}}+2a-48 \\
\end{align}\]
Thus, the standard form of the equation after solving is \[{{a}^{2}}+2a-48\] .

Note:
 While solving the above equation perform the multiplication carefully. Do not forget to write the equation in the standard form at the end. Write the solution step by step and don't jump directly to the answer. Do check whether your equation is in a standard form or not. It should be in the form of \[a{{x}^{2}}+bx+c=0\] . Avoid silly mistakes while solving.