MAKE SENSE OF ALGEBRA
Ex1: Expand:
(a) 2(x + 6)
(b) 3(x + 2)
(c) 4(2x + 3)
(d) 10(x – 6)
(e) 4(x – 2)
(f) 3(2x – 3)
(g) 5(y + 4)
(h) 6(4 + y)
(i) 9(y + 2)
(j) 7(2x – 2y)
(k) 2(3x – 2y)
(m) 5(2x – 2y)
(n) 4(y – 4x2)
(o) 9(x2 – y)
(p) 7(4x + x2)
Ex2: Remove the brackets to expand these expressions.
(a) 2x(x + y)
(b) 3y(x – y)
(c) 2x(x + 2y)
(d) 4x(3x – 2y)
(e) xy(x – y)
(f) 3y(4x + 2)
(g) 2xy(9 – 4y)
(h) 2x2(3 – 2y)
(i) 3x2(4 – 4x)
(j) 4xy2(3 – x)
(k) 2x2y(y – 2x)
(l) 4x2y(3 – 2x)
(m) 3xy2(x + y)
(n) x2y(2x + y)
(o) 9x2(9 – 2x)
Ex3: Expand and simplify:
(a) 2(5 + x) + 3x
(b) 3(y – 2) + 4y
(c) 2x + 2(x – 4)
(d) 4x + 2(x – 3)
(e) 2x(4 + x) – 5
(f) 4(x + 2) – 7
(g) 6 + 3(x – 2)
(h) 4x + 2(2x + 3)
(i) 2x + 3 + 2(2x + 3)
(j) 3(2x + 2) – 3x – 4
(k) 6x + 2(x + 3)
(l) 7y + y(x – 4) – 4
Ex4: Expand and simplify:
(a) 2(x – 1) + 4x – 4
(b) 4(x + 40) + 2(x – 3)
(c) 2(x – 2) + 2(x + 3)
(d) 3(x + 2) + 4(x + 5)
(e) 8(x + 10) + 4(3 – 2x)
(f) 4(2x – 3) + (x – 5)
Ex5: Simplify these expressions by removing brackets and collecting like terms.
(a) 2y(2x – 2y + 4)
(b) 2y(5 – 4y) – 4y2
(c) 3x(2x + 4) – 9
(d) 3y(y + 2) – 5y2
(e) 4(x2 + 2) + 2(4 – x2)
(f) 4x(x + 1) + 2x(x + 3)
(g) 3x2(4 – x) + 2(5x2 – 2x3)
(h) x(2x + 3) + 3(5 – 2x)
(i) x(x + y) + x(x – y)
Ex6: Simplify these expressions by removing brackets and collecting like terms.
(a) 3x(4y – 4) + 4(3xy + 4x)
(b) 2x(5y – 4) + 2(6x – 4xy)
(c) 3x(4 – 8y) + 3(2xy – 5x)
(d) 3(6x – 4y) + x(3 – 2y)
(e) x(x – y) + 3(2x – y)
(f) 4(x – 2) + 3x(4 – y)
(g) 2x(x + y) + 2(x2 + 3xy)
(h) 3(4xy – 2x) + 5(3x – xy)
Ex7: Factorise.
(a) 3x + 6
(b) 15y – 12
(c) 8 – 16z
(d) 35 + 25t
(e) 2x – 4
(f) 3x – 7
(g) 18k – 64
(h) 33p + 22
(i) 2x + 4y
(j) 3p – 15q
(k) 13r – 26s
(l) 2p + 4q + 6r
(c) 3x2 + 3x
(d) 15pq + 21p
Ex8: Factorise as fully as possible.
(a) 21u – 49v + 35w
(b) 3xy + 3x
(e) 9m2 – 33m
(f) 90m3 – 80m2
(g) 36x3 + 24x5
(h) 32p2q – 4pq2
Ex9: Factorise as fully as possible
(a) 14m2n2 + 4m3n3
(b)
1
2
a+
3
2
b
(g) 5(x + 1)2 – 4(x + 1)3
(b) 17abc + 30ab2c
3
7
4
8
(c) m3n2 + 6m2n2(8m + n)
(e) x4 + x
(f) 3(x – 4) + 5(x – 4)
(h) 6x3 + 2x4 + 4x5
(i) 7x3y – 14x2y2 + 21xy2
Ex10. Solve the following equations.
(a) 12x + 1 = 7x + 11
(b) 6x + 1 = 7x + 11
(c) 6y + 1 = 3y – 8
(d) 11x + 1 = 12 – 4x
(e) 8 – 8p = 9 – 9p
(f)
1
2
x–7=
1
4
x+8
Ex11. Solve the following equations.
(a) 4(x + 1) = 12
(b) 2(2p + 1) = 14
(c) 8(3t + 2) = 40
(d) 5(m – 2) = 15
(e) -5(n – 6) = -20
(f) 2(p – 1) + 7(3p + 2) = 7(p – 4)
(g) 2(p – 1) – 7(3p – 2) = 7(p – 4)
(h) 3(2x + 5) – (3x + 2) = 10
Ex12. Solve for x.
(a) 7(x + 2) = 4(x + 5)
(b) 4(x – 2) + 2(x + 5) = 14
(c) 7x – (3x + 11) = 6 – (5 – 3x)
(d) -2(x + 2) = 4x + 9
(e) 3(x + 1) = 2(x + 1) + 2x
(f) 4 + 2(2 – x) = 3 – 2(5 – x)
Ex13. Solve the following equations for x.
(a) 33𝑥 = 27
(b) 23𝑥+4 = 32
(d) 43𝑥 = 2𝑥+1
(e) 93𝑥+4 = 274𝑥+3
(c) 52(3𝑥+1) = 625