Question

How do you find the product of $ (7x + 4)(9x + 8) $ ?

Answer 1

Hint: The method can be referred to as the FOIL method because FOIL is a mnemonic for the traditional method of multiplying two binomials. The FOIL procedure is a two-step mechanism that utilizes the distributive law:
 $
  (a + b)(c + d) = a(c + d) + b(c + d) \\
   = ac + ad + bc + bd \;
  $

Complete step-by-step answer:
Two linear equations have been given to us to multiply. The polynomials must be broken in the FOIL order. First-Outside-Inside-Last (FOIL) is an acronym that stands for First-Outside-Inside-Last (FOIL). It's a tool for spreading out polynomial multiplication.
The two terms of the polynomial are $ (7x + 4) $ and $ (9x + 8) $
We begin solving by multiplying the first terms of both the polynomials. The terms are $ 7x $ and $ 9x $ .
So, we get, $ 7x \times 9x = 63{x^2} $
Next, we will solve by multiplying the outside terms of both the polynomials. The terms are $ 7x $ and $ 8 $ .
So, we get, $ 7x \times 8 = 56x $
Then we will solve by multiplying the inside terms of both the polynomials. The terms are $ 4 $ and $ 9x $ .
So, we get, $ 4 \times 9x = 36x $
Finally, we will solve by multiplying the last terms of both the polynomials. The terms are $ 4 $ and $ 8 $ .
So, we get, $ 4 \times 8 = 32 $
Now, we have to add all the terms to get the final solution, so we get,
 $ (7x + 4)(9x + 8) = 63{x^2} + 56x + 36x + 32 $
The product of $ (7x + 4)(9x + 8) $ is equal to $ 63{x^2} + 92x + 32 $
So, the correct answer is “ $ 63{x^2} + 92x + 32 $ ”.

Note: FOIL is an acronym for the product's four terms:
First ("first" values of each binomial are multiplied)
Outer(The first term of the first binomial and the second term of the second binomial are multiplied as "outside" terms)
Inner (the second term of the first binomial and the first term of the second) are multiplied.
Last("last" terms of both the binomials are multiplied)