Question

Use FOIL to multiply the following two polynomials: (2x + 4)(3x + 1)

A. 6x2 + 14x + 4

B. 3x2 + 14x + 4

C. 6x + 14x + 4

D. 6x2 + 14x + 8

Answer 1

the answer is D. 6x2 + 14x + 8

Answer 2

Given: (2x+4)(3x+1)

Multiply the two binomials using the FOIL method. FOIL is an acronym for the order in which we multiply terms in a binomial. FOIL stands for: First Outer Inner Last. So, we follow this order: multiply the first outer term by the second binomial, and then multiply the second inner term by the second binomial.

The FOIL method is derived from the Distributive Property, and can be stated Algebraically as:

(a+b)(a+b) ——>a(a+b)+b(a+b). —-—————> a²+ab+ba+b² ——————-> a²+2ab+b²

So, let’s FOIL out (2x+4)(3x+1) to the equivalent trinomial form:

First Outer: 2x(3x+1)

Inner Last: 4(3x+1)

So, we have: 2x(3x+1)+4(3x+1)

Now, distribute and simplify:

6x²+2x+12x+4

Now, simplify:

Answer: 6x²+14x+4