Free Printable Factorisation, Expansion and Algebraic Fraction

1.

Expand/ kembangkan $5x\left(3-2xy\right)$ .

a)

$8x-7x^2y$

b)

$15x-10x^2y$

c)

$15x-2xy$

d)

$8x-10x^2y$

2.

Mark '✓' for the correct for the following expansion.
Tandakan ‘✓’ bagi betul untuk kembangan berikut.

a)

$7m\left(p-3mn\right)\ =\ 7m-21mn$

b)

$\left(k+3\right)\left(5k-6\right)=5k^2+9k-18$

c)

$\left(4x+3\right)^2=16x^2+12x+9$

d)

$\left(2p-3\right)^2=4p^2-12p+9$

3.

Simplify $(f+2h)^2–3(2f–3h)^2=$

a)

$13f^2-32fh+31h^2$

b)

$-11f^2+40fh-23h^2$

c)

$-13f^2+20fh-23h^2$

d)

$11f^2+20fh-23h^2$

4.

What value should be in each box if you need to factorize
$x^2-8x+16$ ?

a)

$p=x^2,\ q=+8x,\ r=+16$

b)

$p=x^2,\ q=+16,\ r=+8x$

c)

$p=x^2,\ q=+16,\ r=-8x$

d)

$p=x^2,\ q=-8x,\ r=+16$

5.

Factorise: $4xw\ +\ 12xz\ -\ 3wy-\ 9yz$

a)

$\left(4x+3y\right)\left(w-3z\right)$

b)

$\left(4x+3y\right)\left(w+3z\right)$

c)

$\left(4x-3y\right)\left(w+3z\right)$

d)

$\left(4x-3y\right)\left(w-3z\right)$

6.

Simplify $\frac{2p+4}{p^2-4}$

a)

$\frac{2}{p-2}$

b)

$\frac{p}{p-2}$

c)

$\frac{2}{2-p}$

d)

$\frac{p}{p-2}$

7.

Express $\frac{3s^2-5}{s}-\frac{2s+9}{7}$ as a single fraction in its simplest form

a)

$\frac{19s^2-9s-35}{7s}$

b)

$\frac{19s^2-9s-35}{s}$

c)

$\frac{3s^2-2s-14}{s}$

d)

$\frac{3s^2-2s+4}{s}$

8.

Express $\frac{2h+3k}{15hk}\div\frac{6h+4k}{25k^2}$ as a single fraction in its simplest form.

a)

$\frac{5k}{6h}$

b)

$\frac{5\left(2h\ +\ 3k\right)}{6\left(3h\ +\ 2k\right)}$

c)

$\frac{5k\left(2h\ +\ 3k\right)}{2h\left(3h\ +\ 2k\right)}$

d)

$\frac{5k\left(2h\ +\ 3k\right)}{6h\left(3h\ +\ 2k\right)}$

9.

simplify the following algebraic fraction

\frac{p^2-1}{3pq}\ \times\frac{q^2}{p-1}

a)

$\frac{p^2+1}{3}$

b)

$\frac{q\left(p+1\right)}{3p}$

c)

$\frac{q}{3+1}$

d)

$q\left(p+1\right)$

10.

$\left(6a+2a\right)-\left(3a-ab\right)$

a)

$3a+3ab$

b)

$9a+ab$

c)

$3a-ab$

d)

$9a+3ab$

11.

Factorise b²- 81.

a)

(b-8)(b+8)

b)

(b-9)(b+9)

c)

(b-9)(b-9)

d)

(b-8)(b-8)

12.

$\frac{3}{p}+\frac{4}{1-p}$

a)

$\frac{3+4p}{1-p}$

b)

$\frac{3+p}{1-p}$

c)

$\frac{3+p}{p\left(1-p\right)}$

d)

$3+4p^2$

13.

Factorise completely : 2x²- 50

a)

2( x - 5 )²

b)

2( x + 5 )( x - 5)

c)

(2x + 5)(2x - 5)

d)

(2x + 5)(x - 5)

14.

Determine the area for the diagrams below using algebraic expressions

a)

10x² - 11x - 6

b)

7x² - 11x - 6

c)

10x² - 19x - 6

d)

10x² + 11x - 6

15.

Expand the expression.

a)

9y²+6y+4

b)

9y+12y+4

c)

9y²+12y+4

d)

9y+6y+4

Factorisation, Expansion and Algebraic Fraction

Total questions: 15

Worksheet time: 17mins

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