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MTH1W Algebraic Expressions & Exponent Laws
Grade 9 Unit 2 — practice questions with full solutions

Collecting like terms, the distributive property, multiplying and dividing monomials, and the exponent laws. This is the single most transferable skill set in the whole course.

MTH1W · Grade 9 Strand C — Algebra 10 core 1 challenge
1Core
Simplify by collecting like terms:   3x + 5y − 7x + 2y
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  1. Group the x terms and the y terms separately.
  2. x terms: 3x − 7x = −4x.
  3. y terms: 5y + 2y = 7y.
  4. Only like terms can be combined — x and y stay apart.
Final answer−4x + 7y
2Core
Expand and simplify:   4(2x − 3) − 2(x + 5)
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  1. Distribute the 4: 8x − 12.
  2. Distribute the −2 — watch the sign on both terms: −2x − 10.
  3. Combine: 8x − 2x = 6x, and −12 − 10 = −22.
Final answer6x − 22
3Core
Simplify:   (3x2y3)(−2xy2)
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  1. Multiply the coefficients: 3 × (−2) = −6.
  2. Add exponents on x: x2 × x1 = x3.
  3. Add exponents on y: y3 × y2 = y5.
Final answer−6x3y5
4Core
Simplify:   12a5b3⁄4a2b
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  1. Divide the coefficients: 12 ÷ 4 = 3.
  2. Subtract exponents on a: a5−2 = a3.
  3. Subtract exponents on b: b3−1 = b2.
Final answer3a3b2
5Core
Simplify:   (2x3)4
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  1. A power outside a bracket applies to every factor inside.
  2. Apply it to the coefficient: 24 = 16.
  3. Apply it to the variable — multiply the exponents: (x3)4 = x12.
  4. A very common error is writing 2x12 and forgetting to raise the 2.
Final answer16x12
6Core
x53Region ARegion BThe two regions together form one large rectangle
The diagram shows one large rectangle split into Region A and Region B. (a) Write an expression for the area of each region. (b) Write and simplify an expression for the total area. (c) Explain what this diagram shows about the distributive property.
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  1. (a) Area of a rectangle is width × height. Region A: 3 × x = 3x. Region B: 3 × 5 = 15.
  2. (b) Total area = 3x + 15.
  3. The whole rectangle has height 3 and total width (x + 5), so its area can also be written as 3(x + 5).
  4. (c) Both expressions describe the same rectangle, so 3(x + 5) = 3x + 15 — this is exactly the distributive property, shown as area.
Final answer(a) 3x and 15   (b) 3x + 15   (c) It shows 3(x + 5) = 3x + 15
7Core
Evaluate 5x2 − 3x + 2 when x = −2.
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  1. Substitute carefully, using brackets around the negative value: 5(−2)2 − 3(−2) + 2.
  2. Powers first: (−2)2 = 4, so the first term is 5(4) = 20.
  3. Second term: −3(−2) = +6.
  4. Add it all: 20 + 6 + 2.
Final answer28
8Core
A rectangle has length (3x + 2) and width (x − 1). Write a simplified expression for its perimeter.
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  1. Perimeter = 2(length) + 2(width).
  2. Substitute: 2(3x + 2) + 2(x − 1).
  3. Expand: 6x + 4 + 2x − 2.
  4. Collect like terms: 8x + 2.
Final answer8x + 2
9Core
Simplify:   1⁄2x + 3⁄4x − 1⁄4x
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  1. All three are like terms, so just combine the fraction coefficients.
  2. Use a common denominator of 4: 2⁄4 + 3⁄4 − 1⁄4.
  3. That gives 4⁄4 = 1.
Final answerx
10Core
Simplify:   (a4b2)(a2b3) ÷ (a3b)
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  1. Multiply the numerator first — add exponents: a4+2b2+3 = a6b5.
  2. Now divide — subtract exponents: a6−3 = a3.
  3. And for b: b5−1 = b4.
Final answera3b4
11Challenge
Expand and simplify fully:   −2(3a − 4b) + 5(2a − b) − (a + 3b)
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  1. Distribute the −2: −6a + 8b.
  2. Distribute the 5: +10a − 5b.
  3. The final bracket has an invisible −1 in front: −a − 3b.
  4. Collect a terms: −6a + 10a − a = 3a.
  5. Collect b terms: 8b − 5b − 3b = 0b, which vanishes.
Final answer3a

MTH1W Algebraic Expressions & Exponent Laws — common questions

Short answers to the things students ask most about this unit.

What are the exponent laws in Grade 9 math?

Multiplying powers with the same base adds exponents; dividing subtracts them; a power of a power multiplies them; and anything to the power zero equals one.

Why is (2x³)⁴ not 2x¹²?

The exponent outside the bracket applies to every factor inside, including the coefficient. So 2 is also raised to the fourth power, giving 16x¹².

More MTH1W practice — grade 9 math

MTH1W Number SenseMTH1W Solving Linear EquationsMTH1W Linear Relations & GraphingMTH1W Geometry & MeasurementAll MTH1W units
← Unit 1: Number SenseUnit 3: Solving Linear Equations →
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