Answer
The product of (3x-5)(4x+7) is
[tex]12x^2+x-35[/tex]
SOLUTION
Problem Statement
The question asks us to find the following product:
[tex](3x-5)(4x+7)[/tex]Method
To solve this question, we need to apply the FOIL Method. The FOIL method is given below:
The diagram shows how to apply the FOIL method.
- First (F) - Multiply the first numbers from both brackets
- Outside (O) - Multiply the two outer values of both brackets i.e. the first value in the first bracket on the left and the last value on the second bracket on the right.
- Inside (I) - Multiply the two inner values of both brackets i.e. the second value in the first bracket and the first value in the second bracket. This is also the same as saying we multiply the middle values
- Last (L) - Multiply the last numbers in both brackets
After performing this multiplication, we add up the result.
Implementation
The product is thus computed below:
[tex]\begin{gathered} (3x-5)(4x+7) \\ \text{Applying the FOIL method:} \\ F-\text{First:} \\ 3x\times4x=12x^2 \\ \\ O-\text{Outside:} \\ 3x\times7=21x \\ \\ I-\text{Inside:} \\ -5\times4x=-20x \\ \\ L-\text{Last:} \\ -5\times7=-35 \\ \\ \text{Adding up the results, we have:} \\ 12x^2+21x-20x-35 \\ =12x^2+x-35 \\ \\ \therefore(3x-5)(4x+7)=12x^2+x-35 \end{gathered}[/tex]Final Answer
The product of (3x-5)(4x+7) is
[tex]12x^2+x-35[/tex]
