Using the FOIL method, find the following four products:

F (product of the first terms): \(\displaystyle 4x \cdot 2x = 8x^{2}\)

O (product of the outer  terms): \(\displaystyle 4x \cdot (-5) = -20x\)

I (product of the inner terms): \(\displaystyle - 7 \cdot 2x = -14x\)

L (product of the last terms):  \(\displaystyle - 7 \cdot (-5) = 35\)

Add the terms and simplify:

\(\displaystyle 8x^{2} + (-20x )+ (-14x ) + 35\)

\(\displaystyle = 8x^{2} -34x + 35\),

the correct choice.

In order to solve this, use the FOIL method to distribute the terms.

\(\displaystyle (2x-3)(x+4) =(2x)(x)+(2x)(4)+(-3)(x)+(-3)(4)\)

Simplify the terms.

\(\displaystyle 2x^2+8x-3x-12\)

Combine like-terms.

The answer is:  \(\displaystyle 2x^2+5x-12\)

Use the FOIL method to distribute:

First: \(\displaystyle 2x \cdot x=2x^2\)

Outer: \(\displaystyle 2x \cdot 4=8x\)

Inner: \(\displaystyle -1 \cdot x = -x\)

Last: \(\displaystyle -1 \cdot 4 = -4\)

Then simply combine like terms.

Use the FOIL method to distribute:

First: \(\displaystyle 3x \cdot 4x = 12x\)

Outer: \(\displaystyle 3x \cdot (-1)=-3x\)

Inner: \(\displaystyle -2 \cdot 4x = -8x\)

Last: \(\displaystyle -2 \cdot (-1) = +2\)

Then simply combine like terms.

Use the FOIL method to distribute:

First: \(\displaystyle 3x \cdot 3x=9x^2\)

Outer: \(\displaystyle 3x \cdot 5=15x\)

Inner: \(\displaystyle 5 \cdot 3x = 15x\)

Last: \(\displaystyle 5 \cdot 5 = +25\)

Then simply combine like terms.

This is also a common pattern (squaring a binomial) with which you should be familiar.

Watch for the common mistake of squaring the terms individually and leaving out the \(\displaystyle +30x\).

Multiply the first term of the first binomial with both terms of the second binomial.  Then add the second term of the first binomial multiplied with both terms of the second binomial.

\(\displaystyle (x+6)(x-12) = (x)(x)+(x)(-12)+(6)(x)+(6)(-12)\)

Simplify the terms.

\(\displaystyle x^2-12x+6x-72\)

Combine like-terms.

The answer is:  \(\displaystyle x^2-6x-72\)

The FOIL method stands for FIRST, OUTER, INNER, LAST. It refers to the terms in the pair of parenthesis. 

We multiply together the

FIRST TERMS: \(\displaystyle 2x*3x=6x^2\)

OUTER TERMS: \(\displaystyle 2x*(-4y)=-8xy\)

INNER TERMS: \(\displaystyle y*3x =3xy\)

LAST TERMS: \(\displaystyle y*(-4y)=-4y^2\)

Adding them up and combining like terms yields 

\(\displaystyle 6x^2-5xy-4y^2\)

The FOIL method to multiply binomials is:

\(\displaystyle (a+b)(c+d) = ac+ad+bc+bd\)

Multiply the given problem using this format.

\(\displaystyle (x+9)(2x-3) = (x)(2x)+(x)(-3)+(9)(2x)+(9)(-3)\)

Simplify the right side.

\(\displaystyle 2x^2-3x+18x-27\)

Combine like-terms.

The answer is:  \(\displaystyle 2x^2+15x-27\)

To simply this expression you must distribute correctly.

Using the FOIL method is the easiest wait to do this, so:

FIRST: \(\displaystyle x*2x=2x^2\)

OUTTER: \(\displaystyle x*-1=-x\)
INNER: \(\displaystyle 2x*1=2x\)
LAST: \(\displaystyle 1*-1=-1\)

Once you combine like-terms you end up with:

\(\displaystyle 2x^2+x-1\)

To do this you must distribute using the FOIL method.

\(\displaystyle (3x+3)(-3x-3)\)

\(\displaystyle -9x^2-9x-9x-9\)

Simplify:

\(\displaystyle -9x^2-18x-9\)