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Algebra Basics Review
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Algebra Basics Review
Simplify, expand and show working where requested. Assume any variable in a denominator is non-zero.
Simplifying and Expanding
1.Simplify 9x − 4x + 2x.
2.Simplify 3(4x − 2) + 5.
3.Simplify 8x² − 5x² + 3x.
4.Expand 4(x − 6).
5.Expand −2(3x + 8).
6.Expand x(x − 9).
7.Expand and simplify 3(x + 2) + 2(x − 5).
8.Expand and simplify 4(2x − 1) − 3(x + 4).
9.Which option is equivalent to 8x − 20?
- 4(2x − 5)
- 2(4x − 5)
- 8(x − 20)
- Both 4(2x − 5) and 2(4x − 5)
Algebraic Manipulation
10.Simplify 12x ÷ 4.
11.Simplify 15x² ÷ 5x.
12.Simplify (18x + 12) ÷ 6.
13.Expand and simplify (x + 4)(x + 3).
14.Expand and simplify (x − 2)(x + 7).
15.A rectangular weather-station sensor panel has length three times x, increased by two metres, and width x plus four metres. Write and simplify an expression for its perimeter.
16.A rectangular weather-station sensor panel has length three times x, increased by two metres, and width x plus four metres. Expand and simplify an expression for its area.
Investigating Powers and Brackets
Use substitution and expansion to test how powers of bracketed expressions behave.
17.Test whether p(q + r)² equals pq² + pr² when p = 3, q = 2 and r = 5. Calculate both sides.
18.Expand (q + r)² first, then multiply by p to expand p(q + r)².
19.Explain why p(q + r)² cannot be expanded by distributing p to only the two squared terms. State the correct expansion.
20.Use a = 1 and b = 2 to show that 3(a + b)³ is not generally equal to 3a³ + 3b³. Then write the correct expansion of 3(a + b)³.
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