Practice Expansion Intuition in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

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Quick Recap

Understanding algebraic expansion as the process of applying the distributive property to multiply out factors and remove parentheses.

Open up the parentheses: (x+2)(x+3)(x + 2)(x + 3) becomes x2+3x+2x+6=x2+5x+6x^2 + 3x + 2x + 6 = x^2 + 5x + 6.

Showing a random 20 of 50 problems.

Example 1

medium
Expand (3x−2)(x+5)(3x-2)(x+5).

Example 2

hard
Use (a+b)(a−b)=a2−b2(a + b)(a - b) = a^2 - b^2 to compute 52⋅4852 \cdot 48 mentally.

Example 3

challenge
Find the constant term in (x+2)(x−1)(x+3)(x + 2)(x - 1)(x + 3).

Example 4

easy
Expand (x+4)2(x+4)^2.

Example 5

challenge
Without full expansion, find the coefficient of xx in (x+1)(x+2)(x+3)(x+4)(x + 1)(x + 2)(x + 3)(x + 4).

Example 6

easy
Expand 5(2x+3)5(2x+3).

Example 7

easy
Expand (x+3)(x+5)(x + 3)(x + 5).

Example 8

easy
Expand −3(x−2)-3(x-2).

Example 9

medium
Expand (2x−1)(2x+1)(2x-1)(2x+1).

Example 10

medium
Expand 5(x−1)−2(3x+4)5(x - 1) - 2(3x + 4).

Example 11

medium
Expand (x+y)(x−y)(x + y)(x - y).

Example 12

medium
Expand (a+b)2(a + b)^2.

Example 13

hard
Expand (x+3)(x−3)(x2+9)(x + 3)(x - 3)(x^2 + 9).

Example 14

easy
Expand (x+1)(x−2)(x+1)(x-2).

Example 15

medium
Expand (3x+5)(2x−1)(3x + 5)(2x - 1).

Example 16

medium
Expand and simplify 2(x+3)+3(x−1)2(x+3)+3(x-1).

Example 17

medium
Expand (x+1)2+(x−1)2(x + 1)^2 + (x - 1)^2.

Example 18

medium
Expand −(x−3)(x+5)-(x - 3)(x + 5).

Example 19

easy
Expand −4(2x−5)-4(2x - 5).

Example 20

easy
Expand (x+2)(x+3)(x+2)(x+3).
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