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:  $\displaystyle 0$

Use the FOIL method to simplify the expression. Multiply each term of the first binomial with the terms of the second binomial.

$\displaystyle (7x)(3)+(7x)(-9x)+(-4)(3)+(-4)(-9x)$

Simplify the expression.

$\displaystyle 21x-63x^2-12+36x$

Combine like-terms and reorder all the terms from highest to lowest order.

The answer is:  $\displaystyle -63x^2+57x-12$

We can expand this expression by using the FOIL method.

Follow the given template and substitute.

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

$\displaystyle (\pi-3)(1-3\pi)$

$\displaystyle =(\pi)(1)+(\pi)(-3\pi)+(-3)(1)+(-3)(-3\pi)$

Simplify the terms.

$\displaystyle =\pi-3\pi^2-3+9\pi$

Combine like-terms.

The answer is:  $\displaystyle -3\pi^2+10\pi-3$

Use the FOIL method to simplify this expression.

Multiply each term of the first binomial with the terms of the second binomial.

$\displaystyle (4)(7) + (4)(6x) + (-x)(7) + (-x)(6x)$

Simplify the expression.

$\displaystyle 28+24x-7x-6x^2$

Combine like terms.

The answer is:  $\displaystyle -6x^2+17x+28$

Use the FOIL method to simplify this expression.  Use the following template:

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

$\displaystyle (\sqrt{3}-3)(\sqrt5-5)$

$\displaystyle = (\sqrt{3})(\sqrt{5 })+(\sqrt{3})(-5)+(-3)(\sqrt{5})+(-3)(-5)$

Simplify each term.  Uncommon radical terms cannot be combined.

The answer is:  $\displaystyle \sqrt{15}-5\sqrt3 -3\sqrt5 +15$

Use the FOIL method to simplify this expression.  Use the following formula as a template to solve the expression:

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

For $\displaystyle (x^2+3)(-9x^2+4)$,

$\displaystyle (x^2)(-9x^2)+(x^2)(4)+(3)(-9x^2)+(3)(4)$

Simplify all the terms.

$\displaystyle -9x^4+4x^2-27x^2+12$

Combine like terms.

The answer is:  $\displaystyle -9x^4-23x^2+12$

Use the FOIL method to simplify this expression.

$\displaystyle (\frac{2}{3}x+3)(\frac{2}{5}x+2)$

$\displaystyle =(\frac{2}{3}x)(\frac{2}{5}x)+(\frac{2}{3}x)(2)+(3)(\frac{2}{5}x)+(3)(2)$

Simplify all the terms in parentheses.

$\displaystyle \frac{4}{15}x^2+\frac{4}{3}x+\frac{6}{5}x+6$

Combine the center two terms.

$\displaystyle \frac{4}{3}x+\frac{6}{5}x = \frac{20}{15}x+\frac{18}{15}x = \frac{38}{15}x$

The answer is:  $\displaystyle \frac{4}{15}x^2+\frac{38}{15}x+6$

Use the FOIL method to simplify this expression.

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

Follow this equation for the given problem.

$\displaystyle (4x-6)(7x+3) = (4x)(7x)+(4x)(3)+(-6)(7x)+(-6)(3)$

Simplify the parentheses.

$\displaystyle 28x^2+12x-42x-18$

Combine like-terms.

The answer is:  $\displaystyle 28x^2-30x-18$

Solve the expression by using the FOIL method.  Follow the template below.

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

$\displaystyle (5x)(3x)+(5x)(-1)+(18)(3x)+(18)(-1)$

Simplify the terms.

$\displaystyle 15x^2-5x+54x-18$

Combine like-terms.

$\displaystyle 15x^2-5x+54x-18 = 15x^2+49x-18$

The answer is:  $\displaystyle 15x^2+49x-18$