Using the FOIL distribution method:

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

First: \(\displaystyle x*x = x^2\)

Outer: \(\displaystyle x*-2= -2x\)

Inner: \(\displaystyle 2*x = 2x\)

Last: \(\displaystyle 2*-2 = -4\)

Resulting in: \(\displaystyle x^2 - 2x + 2x -4\)

Combining like terms, the \(\displaystyle x\)'s cancel for a final answer of:

\(\displaystyle x^{2} - 4\)

Using the FOIL distribution method:

\(\displaystyle (x+2)(x+3)\)

First: \(\displaystyle x*x = x^2\)

Outer: \(\displaystyle x*3= 3x\)

Inner: \(\displaystyle 2*x = 2x\)

Last: \(\displaystyle 2*3=6\)

Resulting in: \(\displaystyle x^2 +3x+2x+6\)

Combining like terms, the \(\displaystyle x\)'s combine for a final answer of:

\(\displaystyle x^{2} +5x +6\)

Using the FOIL distribution method:

\(\displaystyle (x-4)(x-7)\)

First: \(\displaystyle x*x = x^2\)

Outer: \(\displaystyle x*-7= -7x\)

Inner: \(\displaystyle -4*x = -4x\)

Last: \(\displaystyle -4*-7=28\)

Resulting in: \(\displaystyle x^2 -4x-7x+28\)

Combining like terms, the \(\displaystyle x\)'s combine for a final answer of:

\(\displaystyle x^{2} -11x +28\)

Using the FOIL distribution method:

\(\displaystyle (x+5)(x-8)\)

First: \(\displaystyle x*x = x^2\)

Outer: \(\displaystyle x*-8= -8x\)

Inner: \(\displaystyle 5*x = 5x\)

Last: \(\displaystyle 5*-8=-40\)

Resulting in: \(\displaystyle x^2 -8x+5x-40\)

Combining like terms, the \(\displaystyle x\)'s combine for a final answer of:

\(\displaystyle x^{2} -3x-40\)

Using the FOIL distribution method:

\(\displaystyle (x-2)(x+10)\)

First: \(\displaystyle x*x = x^2\)

Outer: \(\displaystyle x*10= 10x\)

Inner: \(\displaystyle -2*x = -2x\)

Last: \(\displaystyle -2*10=-20\)

Resulting in: \(\displaystyle x^2 +10x-2x-20\)

Combining like terms, the \(\displaystyle x\)'s combine for a final answer of:

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

Using the FOIL distribution method:

\(\displaystyle (50+2)(50+2)\)

First: \(\displaystyle 50*50 = 2500\)

Outer: \(\displaystyle 50*2= 100\)

Inner: \(\displaystyle 2*50 = 100\)

Last: \(\displaystyle 2*2=4\)

Resulting in: \(\displaystyle 2500 + 100 +100 +4 = 2704\)

Using the FOIL distribution method:

\(\displaystyle (30+3)(40+4)\)

First: \(\displaystyle 30*40 = 1200\)

Outer: \(\displaystyle 30*4= 120\)

Inner: \(\displaystyle 3*40 = 120\)

Last: \(\displaystyle 3*4=12\)

Resulting in: \(\displaystyle 1200 + 120 +120 +12 = 1452\)

Using the FOIL distribution method:

\(\displaystyle (5x + t)(2x + 3t)\)

First: \(\displaystyle 5x*2x = 10x^2\)

Outer: \(\displaystyle 5x*3t= 15x t\)

Inner: \(\displaystyle t*2x = 2xt\)

Last: \(\displaystyle t*3t=3t^2\)

Resulting in: \(\displaystyle 10x^2 + 15xt + 2xt + 3t^2\)

Combining like terms, the \(\displaystyle xt\)'s combine for a final answer of:

\(\displaystyle 10x^2 + 17xt + 3t^2\)

Using the FOIL distribution method:

\(\displaystyle (x + y)(x - y)\)

First: \(\displaystyle x*x = x^2\)

Outer: \(\displaystyle x*-y= -xy\)

Inner: \(\displaystyle y*x = xy\)

Last: \(\displaystyle y*-y=-y^2\)

Resulting in: \(\displaystyle x^2 - xy + xy - y^2\)

Combining like terms, the \(\displaystyle xy\)'s cancel for a final answer of:

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

Expressions of this form are commonly referred to as "difference of squares". If you can spot them, they are easy to expand and to factor because the middle terms always cancel.

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

Outside: \(\displaystyle (x)(-2)=-2x\)

Inside: \(\displaystyle (x)(7)=7x\)

Last: \(\displaystyle (-2)(7)=-14\)

Add the values together and combine like terms:

\(\displaystyle x^2-2x+7x-14=x^2+5x-14\)