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## 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.

See some of our other supported math practice problems.

### Complexity=5, Mode=single

Expand the following expressions using the FOIL method.
Combine any like terms, but when that is not possible, be sure to follow the order of FOIL: First + Outer + Inner + Last. e.g.
(w+5x)(y+6z) = wy + 6wz + 5xy + 30xz
You don't need multiplication signs.
As you level up, you will need to put variables in alphabetical order, such as xy (not yx).
Use '^' before exponents, such as x^2 for x2.

 1.   (4x - 1)(-2x + 5) 2.   (-x - 5)(-x - 1)

### Complexity=8, Mode=two

Expand the following expressions using the FOIL method.
Combine any like terms, but when that is not possible, be sure to follow the order of FOIL: First + Outer + Inner + Last. e.g.
(w+5x)(y+6z) = wy + 6wz + 5xy + 30xz
You don't need multiplication signs.
As you level up, you will need to put variables in alphabetical order, such as xy (not yx).
Use '^' before exponents, such as x^2 for x2.

 1.   (-3x + y)(4x + 7y) 2.   (-2x + y)(-3x - 5y)

### Complexity=10, Mode=mixed

Expand the following expressions using the FOIL method.
Combine any like terms, but when that is not possible, be sure to follow the order of FOIL: First + Outer + Inner + Last. e.g.
(w+5x)(y+6z) = wy + 6wz + 5xy + 30xz
You don't need multiplication signs.
As you level up, you will need to put variables in alphabetical order, such as xy (not yx).
Use '^' before exponents, such as x^2 for x2.

 1.   (9t - 3u)(4h - s) 2.   (-6z + 2a)(-10f + 10j)

### Complexity=4, Mode=special

Expand the following expressions using the FOIL method.
Combine any like terms, but when that is not possible, be sure to follow the order of FOIL: First + Outer + Inner + Last. e.g.
(w+5x)(y+6z) = wy + 6wz + 5xy + 30xz
You don't need multiplication signs.
As you level up, you will need to put variables in alphabetical order, such as xy (not yx).
Use '^' before exponents, such as x^2 for x2.

 1.   (4x + y)(4x - y) 2.   (3x + 3y)2

### Complexity=10

Expand the following expressions using the FOIL method.
Combine any like terms, but when that is not possible, be sure to follow the order of FOIL: First + Outer + Inner + Last. e.g.
(w+5x)(y+6z) = wy + 6wz + 5xy + 30xz
You don't need multiplication signs.
As you level up, you will need to put variables in alphabetical order, such as xy (not yx).
Use '^' before exponents, such as x^2 for x2.

 1.   (4x - 7y)(2x - 3y) 2.   (-5x + 8y)(-5x + 3y)

### Complexity=5, Mode=single

Expand the following expressions using the FOIL method.
Combine any like terms, but when that is not possible, be sure to follow the order of FOIL: First + Outer + Inner + Last. e.g.
(w+5x)(y+6z) = wy + 6wz + 5xy + 30xz
You don't need multiplication signs.
As you level up, you will need to put variables in alphabetical order, such as xy (not yx).
Use '^' before exponents, such as x^2 for x2.

1(4x - 1)(-2x + 5)
Solution
 First + Outer + Inner + Last (4x)(-2x) + (4x)(5) + (-1)(-2x) + (-1)(5)
Simplify to get - 8x 2 + 22x - 5
2(-x - 5)(-x - 1)
Solution
 First + Outer + Inner + Last (-x)(-x) + (-x)(-1) + (-5)(-x) + (-5)(-1)
Simplify to get x 2 + 6x + 5

### Complexity=8, Mode=two

Expand the following expressions using the FOIL method.
Combine any like terms, but when that is not possible, be sure to follow the order of FOIL: First + Outer + Inner + Last. e.g.
(w+5x)(y+6z) = wy + 6wz + 5xy + 30xz
You don't need multiplication signs.
As you level up, you will need to put variables in alphabetical order, such as xy (not yx).
Use '^' before exponents, such as x^2 for x2.

1(-3x + y)(4x + 7y)
Solution
 First + Outer + Inner + Last (-3x)(4x) + (-3x)(7y) + (y)(4x) + (y)(7y)
Simplify to get - 12x 2 - 17xy + 7y 2
2(-2x + y)(-3x - 5y)
Solution
 First + Outer + Inner + Last (-2x)(-3x) + (-2x)(-5y) + (y)(-3x) + (y)(-5y)
Simplify to get 6x 2 + 7xy - 5y 2

### Complexity=10, Mode=mixed

Expand the following expressions using the FOIL method.
Combine any like terms, but when that is not possible, be sure to follow the order of FOIL: First + Outer + Inner + Last. e.g.
(w+5x)(y+6z) = wy + 6wz + 5xy + 30xz
You don't need multiplication signs.
As you level up, you will need to put variables in alphabetical order, such as xy (not yx).
Use '^' before exponents, such as x^2 for x2.

1(9t - 3u)(4h - s)
Solution
 First + Outer + Inner + Last (9t)(4h) + (9t)(-s) + (-3u)(4h) + (-3u)(-s)
Simplify to get 36ht - 9st - 12hu + 3su
2(-6z + 2a)(-10f + 10j)
Solution
 First + Outer + Inner + Last (-6z)(-10f) + (-6z)(10j) + (2a)(-10f) + (2a)(10j)
Simplify to get 60fz - 60jz - 20af + 20aj

### Complexity=4, Mode=special

Expand the following expressions using the FOIL method.
Combine any like terms, but when that is not possible, be sure to follow the order of FOIL: First + Outer + Inner + Last. e.g.
(w+5x)(y+6z) = wy + 6wz + 5xy + 30xz
You don't need multiplication signs.
As you level up, you will need to put variables in alphabetical order, such as xy (not yx).
Use '^' before exponents, such as x^2 for x2.

1(4x + y)(4x - y)
Solution
FOIL Method

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

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

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

2(3x + 3y)2
Solution
FOIL Method

(3x + 3y)(3x + 3y)
9x2 + 9xy + 9xy + 9y2
9x 2 + 18xy + 9y 2

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

In this case, a = 3x and b = 3y.
Using substitution, we get
(3x)2 + 2(3x)(3y) + (3y)2
9x 2 + 18xy + 9y 2

### Complexity=10

Expand the following expressions using the FOIL method.
Combine any like terms, but when that is not possible, be sure to follow the order of FOIL: First + Outer + Inner + Last. e.g.
(w+5x)(y+6z) = wy + 6wz + 5xy + 30xz
You don't need multiplication signs.
As you level up, you will need to put variables in alphabetical order, such as xy (not yx).
Use '^' before exponents, such as x^2 for x2.

1(4x - 7y)(2x - 3y)
Solution
 First + Outer + Inner + Last (4x)(2x) + (4x)(-3y) + (-7y)(2x) + (-7y)(-3y)
Simplify to get 8x 2 - 26xy + 21y 2   