Test: Expanding brackets - Year 8 MCQ

Simplify the left side by combining like terms: -13b + b = -12b, so the equation becomes -12b - 16 = 1.

To isolate the term with b, add 16 to both sides: -12b - 16 + 16 = 1 + 16 -12b = 17

The equivalent equation is -12b = 17.

Expand the brackets: 4(x - 5) = 4x - 20, so the equation is 4x - 20 = 10.

Add 20 to both sides to isolate the term with x: 4x - 20 + 20 = 10 + 20 4x = 30

Divide both sides by 4: x = 30 / 4 = 7.5

Thus, x = 7.5 (Option B).

Write the equation as 3a + 4 = 6 (assuming "3 x a" means 3a).

To isolate the term with a, subtract 4 from both sides: 3a + 4 - 4 = 6 - 4 3a = 2

The equivalent equation is 3a = 6 - 4 (Option A).

Expand the brackets by distributing the 5: 5(a - 4) = 5 * a - 5 * 4 = 5a - 20

The equivalent expression is 5a - 20 (Option B).

To isolate b, subtract 3a from both sides: 3a + 6 + b - 3a = 3a + 5 - 3a 6 + b = 5

Subtract 6 from both sides: b = 5 - 6 b = -1

This can be written as b = 3a - 3a + 5 - 6, which simplifies to b = -1 (Option A).

Factor the expression 2x - 6: 2x - 6 = 2(x - 3)

Option B (2(x - 3)) is correct.

Distribute the 3 across the terms inside the parentheses: 3(x + 2) = 3 * x + 3 * 2 = 3x + 6

The simplified expression is 3x + 6 (Option A).

Distribute the 2 across the terms inside the parentheses: 2(3y - 4) = 2 * 3y - 2 * 4 = 6y - 8

The equivalent expression is 6y - 8 (Option A).

Expand the left side: 4(a + 3) = 4 * a + 4 * 3 = 4a + 12

Expand the right side: 5(b - 8) = 5 * b - 5 * 8 = 5b - 40

The expanded equation is 4a + 12 = 5b - 40 (Option C).

Distribute the 4 across the terms inside the parentheses: 4(2a - 3) = 4 * 2a - 4 * 3 = 8a - 12

The simplified expression is 8a - 12 (Option B).