Question

How do you simplify \[\left( w-3 \right)\left( w-5 \right)\]?

Answer 1

Hint: In this problem, we have to simplify the given two terms by combining them. We know that we have to multiply the given two factors. We can use the FOIL method to simplify the terms. We know that FOIL means First Outer Inner Last, where we multiply first two terms and the outer terms and the inner terms and last terms. We can then combine the terms from FOIL to get the simplified form.

Complete step-by-step answer:
We know that the given terms to be simplified is,
\[\left( w-3 \right)\left( w-5 \right)\]
We can now use the FOIL method, to multiply the two terms where we multiply first two terms then the outer terms and the inner terms and last terms.
We can apply the FOIL method, we get
First \[\Rightarrow w\times w={{w}^{2}}\]
Outer \[\Rightarrow w\times -5=-5w\]
Inner \[\Rightarrow -3\times w=-3w\]
Last \[\Rightarrow -3\times -5=15\]
We can now combine the above terms, we get
\[\Rightarrow {{w}^{2}}-5w-3w+15\]
We can now simplify the above terms, we get
\[\Rightarrow {{w}^{2}}-8w+15\]
Therefore, the simplified form of \[\left( w-3 \right)\left( w-5 \right)\] is \[{{w}^{2}}-8w+15\] .

Note: We should always remember that We can now use the FOIL method, to multiply the two terms where we multiply first two terms then the outer terms and the inner terms and last terms. We should also concentrate while combining the terms from the FOIL method. We should multiply each term in the first bracket with each term inside the second bracket and combine them to get the simplified form.