Math Practice Problems

Foil Method - Sample Math Practice Problems

The math problems below can be generated by MathScore.com, a math practice program for schools and individual families. References to complexity and mode refer to the overall difficulty of the problems as they appear in the main program. In the main program, all problems are automatically graded and the difficulty adapts dynamically based on performance. Answers to these sample questions appear at the bottom of the page. This page does not grade your responses.

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Complexity=5, Mode=single

Expand the following expressions using the foil method. Don't put multiplication signs between variables and use '^' for exponents. Also, be sure to follow the order of FOIL-First, Outer, Inner, Last
i.e. (x+5)(x+6): x^2 + 11x + 30

1. (3x - 5)(3x - 4)

2. (2x - 4)(3x - 3)

Complexity=8, Mode=two

1. (-8x - 8y)(2x + 8y)

2. (-7x - 7y)(8x - 5y)

Complexity=10, Mode=mixed

1. (-w - 3p)(-8h + 9p)

2. (-8b - 5u)(7w - 10u)

Complexity=4, Mode=special

1. (3x + 2y)²

2. (4x - 2y)²

Complexity=10

1. (-5z - 8y)(-5n + 9r)

2. (7s + 3j)(-10x - 10t)

Answers

Complexity=5, Mode=single

Problem

Correct Answer

Your Answer

(3x - 5)(3x - 4)

Solution

First	+	Outer	+	Inner	+	Last
(3x)(3x)	+	(3x)(-4)	+	(-5)(3x)	+	(-5)(-4)

Simplify to get 9x² - 27x + 20

Problem

Correct Answer

Your Answer

(2x - 4)(3x - 3)

Solution

First	+	Outer	+	Inner	+	Last
(2x)(3x)	+	(2x)(-3)	+	(-4)(3x)	+	(-4)(-3)

Simplify to get 6x² - 18x + 12

Complexity=8, Mode=two

Problem

Correct Answer

Your Answer

(-8x - 8y)(2x + 8y)

Solution

First	+	Outer	+	Inner	+	Last
(-8x)(2x)	+	(-8x)(8y)	+	(-8y)(2x)	+	(-8y)(8y)

Simplify to get ^-16x² - 80xy - 64y²

Problem

Correct Answer

Your Answer

(-7x - 7y)(8x - 5y)

Solution

First	+	Outer	+	Inner	+	Last
(-7x)(8x)	+	(-7x)(-5y)	+	(-7y)(8x)	+	(-7y)(-5y)

Simplify to get ^-56x² - 21xy + 35y²

Complexity=10, Mode=mixed

Problem

Correct Answer

Your Answer

(-w - 3p)(-8h + 9p)

Solution

First	+	Outer	+	Inner	+	Last
(-w)(-8h)	+	(-w)(9p)	+	(-3p)(-8h)	+	(-3p)(9p)

Simplify to get 8hw - 9pw + 24hp - 27p²

Problem

Correct Answer

Your Answer

(-8b - 5u)(7w - 10u)

Solution

First	+	Outer	+	Inner	+	Last
(-8b)(7w)	+	(-8b)(-10u)	+	(-5u)(7w)	+	(-5u)(-10u)

Simplify to get ^-56bw + 80bu - 35uw + 50u²

Complexity=4, Mode=special

Problem

Correct Answer

Your Answer

(3x + 2y)²

Solution
FOIL Method

(3x + 2y)(3x + 2y)
9x² + 6xy + 6xy + 4y²
9x² + 12xy + 4y²

Special Rule: (a + b)² = a² + 2ab - b²

In this case, a = 3x and b = 2y.
Using substitution, we get
(3x)² + 2(3x)(2y) + (2y)²
9x² + 12xy + 4y²

Problem

Correct Answer

Your Answer

(4x - 2y)²

Solution
FOIL Method

(4x - 2y)(4x - 2y)
16x² - 8xy - 8xy + 4y²
16x² - 16xy + 4y²

Special Rule: (a - b)² = a² - 2ab + b²

In this case, a = 4x and b = 2y.
Using substitution, we get
(4x)² - 2(4x)(2y) + (2y)²
16x² - 16xy + 4y²

Complexity=10

Problem

Correct Answer

Your Answer

(-5z - 8y)(-5n + 9r)

Solution

First	+	Outer	+	Inner	+	Last
(-5z)(-5n)	+	(-5z)(9r)	+	(-8y)(-5n)	+	(-8y)(9r)

Simplify to get 25nz - 45rz + 40ny - 72ry

Problem

Correct Answer

Your Answer

(7s + 3j)(-10x - 10t)

Solution

First	+	Outer	+	Inner	+	Last
(7s)(-10x)	+	(7s)(-10t)	+	(3j)(-10x)	+	(3j)(-10t)

Simplify to get ^-70sx - 70st - 30jx - 30jt

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