Question

How do you find the product of \[\left( a+5 \right)\left( a-6 \right)?\]

Answer 1

Hint: As you can see that we have to do the multiplication of \[\left( a+5 \right)\left( a-6 \right)\] term. You have to use the FOIL method for the multiplication.
FOIL method refers to
F = First term
O = Outer term
I = Inner term
L = Last term

Complete step by step solution:
As we know that, given term is \[\left( a+5 \right)\left( a-6 \right).\]
Here, you have to multiply the given term by applying the FOIL method.
\[(i)\]First Term\[:-a\times a={{a}^{2}}\]
Above we have multiplied the first term of the given equation.
\[(ii)\]Outer Term\[:-a\times \left( -6a \right)=-6a\]
Above we have multiplied the outer term of the given equation.
\[(iii)\]Inner Term\[:-5\times a=5a\]
Above we have multiplied the inner term of the given equation.
\[(iv)\]Last term\[:-5\times \left( -6 \right)=-30\]
Above we have multiplied the last term of the given equation.
Now, we have to arrange the above terms in terms of the equation. Therefore the equation will be,\[{{a}^{2}}-6a+5a-30\]
Here combine the like terms and write the equation in standard form that is \[a{{x}^{2}}+bx+c.\]
Hence by simplifying the given equation,
\[\therefore {{a}^{2}}-a-30\]

Hence the product of \[\left( a+5 \right)\left( a-6 \right)\] is \[{{a}^{2}}-a-30.\]

Note: Remember that we have to multiply the given term only by FOIL method as it is easy to solve and also is the time. After applying the \['FOIL\,method'\]you have to write the equation in the standard form.