Use the FOIL method to simplify this expression. 

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

Rewrite the terms.

\(\displaystyle (10x)(2)+(10x)(-3x)+(-1)(2)+(-1)(-3x)\)

The expression becomes:

\(\displaystyle 20x-30x^2-2+3x\)

Combine like terms.

The answer is:  \(\displaystyle -30x^2+23x-2\)

Use the FOIL method to solve this problem.

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

\(\displaystyle (\sqrt3)(\sqrt2)+(\sqrt3)(-\sqrt3)+(-\sqrt2)(\sqrt2)+(-\sqrt2)(-\sqrt3)\)

Multiply the terms together.

\(\displaystyle \sqrt6-3-2+\sqrt6\)

Combine like-terms.

The answer is:  \(\displaystyle 2\sqrt6-5\)

Solve the binomials by using the FOIL method.  Following the template given:

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

\(\displaystyle (\sqrt8)(\sqrt8)+(\sqrt8)(6)+(-3)(\sqrt8)+(-3)(6)\)

Simplify the expression.

\(\displaystyle 8+6\sqrt8-3\sqrt8-18\)

Combine like-terms.

\(\displaystyle 3\sqrt8 -10\)

We can rewrite \(\displaystyle \sqrt8\) using common factors.

\(\displaystyle \sqrt8 =\sqrt 4\cdot \sqrt2 = 2\sqrt2\)

\(\displaystyle 3(2\sqrt2) -10 = 6\sqrt2-10\)

The answer is:  \(\displaystyle 6\sqrt2-10\)

Solve this expression using the FOIL method.

Use the following template for the FOIL method:

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

Rewrite \(\displaystyle (9-3x)(-2-8x)\).

\(\displaystyle (9)(-2)+(9)(-8x)+(-3x)(-2)+(-3x)(-8x)\)

Simplify the terms.

\(\displaystyle -18-72x+6x+24x^2\)

Combine like-terms and reorder the expression from highest to lowest power.

The answer is:  \(\displaystyle 24x^2-66x-18\)

Simplify by using the FOIL method.  Follow the template below to solve the problem.

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

\(\displaystyle (e^2+3)(e-1) = (e^2)(e)+ (e^2)(-1)+(3)(e)+(3)(-1)\)

Simplify the terms.

\(\displaystyle e^3-e^2+3e-3\)

Do not combine unlike terms.

The answer is:  \(\displaystyle e^3-e^2+3e-3\)

Use the FOIL method to solve this expression.

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

Write out the terms.

\(\displaystyle (5-\sqrt8)(4-\sqrt2)\)

\(\displaystyle =(5)(4)+(5)(-\sqrt2)+(-\sqrt8)(4)+(-\sqrt8)(-\sqrt2)\)

Simplify the terms.

\(\displaystyle =20-5\sqrt2-4\sqrt8+\sqrt{16}\)

Rewrite the radicals that are not simplified.

\(\displaystyle \sqrt8 = \sqrt{4\times 2} = \sqrt4 \times \sqrt2 = 2\sqrt2\)

\(\displaystyle \sqrt{16}=4\)

Replace the terms.

\(\displaystyle =20-5\sqrt2-4(2\sqrt2)+4\)

\(\displaystyle = 20-5\sqrt2-8\sqrt2+4 = 24-13\sqrt2\)

The answer is:  \(\displaystyle 24-13\sqrt2\)

Solve this by using the FOIL method.

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

Substitute the given terms by the given formula.

\(\displaystyle (9x-8)(10x-7)\)

\(\displaystyle = (9x)(10x)+ (9x)(-7)+(-8)(10x)+(-8)(-7)\)

Simplify the terms.

\(\displaystyle 90x^2-63x-80x+56\)

Combine like-terms.

The answer is:  \(\displaystyle 90x^2-143x+56\)

Use the FOIL method to expand the binomials.

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

Simplify the terms.

\(\displaystyle 54-18x-18x+6x^2\)

Combine like terms.

The answer is:  \(\displaystyle 6x^2-36x+54\)

Solve this expression by using the FOIL method.

\(\displaystyle (-2x)(3x)+(-2x)(-9)+(5)(3x)+(5)(-9)\)

Simplify each term by order of operations.

\(\displaystyle -6x^2+18x+15x-45\)

Combine like-terms.

The answer is:  \(\displaystyle -6x^2+33x-45\)

Use the FOIL method to expand the terms. Follow the template for using this method.

\(\displaystyle (w+x)(y+z) = wy+wz+xy+xz\)

\(\displaystyle (\frac{1}{\sqrt2}-\sqrt2)(\frac{2}{\sqrt2}-\sqrt2)\)

\(\displaystyle (\frac{1}{\sqrt2})(\frac{2}{\sqrt2})+(\frac{1}{\sqrt2})(-\sqrt2)+(-\sqrt2)(\frac{2}{\sqrt2})+(-\sqrt2)(-\sqrt2)\)

Simplify all the terms.

\(\displaystyle 1-1-2+2 = 0\)

The answer is:  \(\displaystyle 0\)