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:

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

Here we have to use the distributive property and FOIL when we are multiplying the two terms. First we multipy the terms in the binomial with the trinomial. Then we add or subtract the coefficients of the terms with same combination of variables x and y.

\(\displaystyle (x+3y) (y^2+3xy+2)\)

\(\displaystyle = x(y^2+3xy+2) +3y(y^2+3xy+2)\)

\(\displaystyle = xy^2+3x^2y+2x +3y^3+9xy^2+6y\)

\(\displaystyle = 3y^3+10xy^2+3x^2y+2x+6y\)

Use the FOIL method to multiply the terms.

\(\displaystyle (3x-6)(3-x) = (3x)(3) +(3x)(-x)+(-6)(3)+(-6)(-x)\)

Simplify the terms on the right side of the equation.

\(\displaystyle 9x-3x^2-18+6x\)

Combine like-terms.

The answer is:  \(\displaystyle -3x^2+15x-18\)

As we know, FOIL stands for First, Outside, Inside, Last, which indicates the order in which we should multiply each of these terms.

First: \(\displaystyle 4x\cdot2x=8x^{2}\)

Outside: \(\displaystyle 4x\cdot-6=-24x\)

Inside: \(\displaystyle 3\cdot2x=6x\)

Last: \(\displaystyle 3\cdot-6=-18\)

We then combine like terms, which in this case are \(\displaystyle -24x\) and \(\displaystyle 6x\). When we add these together, we are left with a trinomial of \(\displaystyle 8x^{2}-18x-18\). None of the remaining terms are alike, so there is no further simplification possible.

To expand this set of binomials we need to FOIL the terms. FOIL is the multiplication steps that need to be applied to a set of binomials.

\(\displaystyle (5-4x)(-3+x)\)

First:  \(\displaystyle 5\cdot -3=-15\)

Outer:  \(\displaystyle 5\cdot x=5x\)

Inner:\(\displaystyle -4x\cdot-3=12x\)

Last:\(\displaystyle -4x\cdotx=-4x^{2}\)

\(\displaystyle $Sum$ =-15+5x+12x-4x^2 = -4x^2+17x-15\)

Use the FOIL method to multiply the polynomials:

(3x+4)(x-2)

 F - Multiply the first terms of each binomial

\(\displaystyle 3x * x = 3x^2\)

O- Multiply the outside terms of each binomial

\(\displaystyle 3x*-2 = -6x\)

I- Multiply the inside terms of each binomial

 \(\displaystyle 4*x=4x\)

L- Multiply the last terms of each binomial

\(\displaystyle 4*-2=-8\)

Add all of the answers and combine like terms

\(\displaystyle 3x^2-6x+4x-8\)

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

Use FOIL to distribute each term.

F: \(\displaystyle 3x(4y)=12xy\)

O: \(\displaystyle 3x(7)=21x\)

I: \(\displaystyle -8(4y)=-32y\)

L:\(\displaystyle -8(7)=-56\)

If possible, combine like terms (none in this case).

\(\displaystyle 12xy+21x-32y-56\)