Year 8 Algebraic Techniques Revision

• This is a Year 8 revision sheet on algebraic techniques.

Question 1

• If m = 5 and n = 3, the value of (m + n)² is to be determined.

Question 2

• Simplify -3m+2mn-4m+5mn.

Question 3

• Simplify 5a x 4b x 2b.

Question 4

• Simplify 18pqr ÷ 3pq.

Question 5

• Expand 4(7-5c).

Question 6

• Expand 2a(a+b).
• The possible answers are:
• 2a² + ab
• 2ab
• 2a² + 2ab
• 2a²b

Question 7

• Expand and simplify 2x² + x(5x - 2).
• The possible answers are:
• 3x² + 10x
• 2x² + 10x
• 7x² - 2x
• 7x + 2x

Question 8

• Expand and simplify 8(m-3) + 3(2m + 4).
• The possible answers are:
• 14m - 12
• 10m - 16
• 14m - 20
• 14m + 36

Question 9

• Expand and simplify 2a(a+b)-b(2a+b).
• Determine what goes in the following spaces:
• a² + ___
• ab - ___
• ___ - b²
• The final answer should be in the form:
• a² - b²

Question 10

• Factorise -8x - 12 and express it in the form (2x + 3).
• The remaining factor needs to be determined.

Question 11

• If a = 0.4, b = -0.5 and c = -3, find the value of (5a + 4b) / c.

Question 12

• If a = 5 and b = 6, find the value of √(2a + b).

Question 13

• Simplify 8xy - 4xp - 6xy - 5xp.
• The possible answers are:
• 2xp - 9xy
• 2xy - 9xp
• 9xp + 2xy

Question 14

• Simplify y² + 7x² + 6y² - 8x².
• The possible answers are:
• -x² + 7y²
• -7x² + y²
• -y² + 7x²

Question 15

• Simplify d x e x u x x.
• The possible answers are:
• deux
• de²ux
• de + ux
• 2deu

Question 16

• Simplify 4mx - 3mn x -m.
• The possible answers are:
• 3m - 3mn
• 12m³n
• 12mn

Question 17

• Simplify 5a x 4b ÷ 2.

Question 18

• Simplify 2a x 6b ÷ 3ab.

Question 19

• Expand 2(3a + 2b + 4c).
• The possible answers are:
• 6a + 4b + 8c
• 6a + 2b + 4c
• 18abc
• 3a + 4b + 8c

Question 20

• Expand 5(3a + 5b - c).
• The possible answers are:
• 3a + 25b - 5c
• 15a + 25b - 5c
• 3a + 5b - 5c
• 15a + 5b - c

Question 21

• Expand -3(2 + a).

Question 22

• Expand -2(2x - 3y + 4).
• The possible answers are:
• -4x + 8y - 6
• 4x + 6y - 8
• -24xy
• -4x + 6y - 8

Question 23

• Expand and simplify 5x(x - 2) + 3(2x - 6).
• The possible answers are:
• 5x² - 18x
• 5x² - 4x
• 5x² - 4x - 18
• 10x² - 3x - 12

Question 24

• Expand and simplify 4(x - y) - 2(y - x) + 3x(y - 2).
• The possible answers are:
• 4xy - 2
• 2xy + 5x
• 3xy - 6y
• 3xy

Question 25

• Expand and simplify 5a² - 2a(2a + b - 3).
• The possible answers are:
• 6a² - 2ab + 4
• 2a² + 6ab
• a² + 6ab - 2a
• a² - 2ab + 6a

Question 26

• Expand and simplify 3a(a - 4) - 2a(a + 2).
• The possible answers are:
• a² - 16a
• 2a² + 6a
• 16a² - 2a
• a² + 12a

Question 27

• Expand and simplify 2m(m + n) - n(2m + n).
• The possible answers are:
• m² - 2n²
• 2m² + n²
• 2m² - n²

Question 28

• Expand and simplify: 2x(x+y) + 3x (x−y)
• Determine what goes in the following spaces:
• x²+___
• xy+___
• x²-___
• The final answer should be in the form:
• x²- xy

Question 29

• Factorise fully 4m² + 8mp.
• The possible answers are:
• 2m(2m + 3p)
• 2m(m + 4p)
• 4m(m + 2p)

Question 30

• Factorise fully ax + xy + x².
• The possible answers are:
• x(2y + x)
• a(a + 2x + y)
• x(a + y + x)