Free Printable Expansions

1.

Expand 2(x + 3).

a)

2x + 3

b)

x + 6

c)

2x + 6

d)

x + 3

2.

Expand $a\left(a+1\right)$ .

a)

$a^2+a$

b)

$a^2+1$

c)

$2a$

d)

$a+1$

3.

Expand $a\left(b+c+d\right)$

a)

$ab+c+d$

b)

$abcd$

c)

$ab+ac+ad$

d)

$ab+cd$

4.

Expand $2g\left(3g+2\right)$

a)

$6g+4g$

b)

$6g+2$

c)

$6g^2+4g$

d)

$10g$

5.

Expand $-4y(2x+3)$ .

a)

$-8xy-12y$

b)

$-8xy+12y$

c)

I don’t know 😓

6.

Expand $2x(y+z)+3x(2y+z)$ .

a)

$x(8y+5)$

b)

$8yx+6z$

c)

$5xz+8xy$

d)

I don’t know 😓

7.

Expand $(x+2y)(x+3y)$ .

a)

$5x^2y^2+x^2+6y^2$

b)

$x^2+6y^2+5x^2y^2$

c)

$x^2+5xy+6y^2$

d)

I don’t know 😓

8.

Expand $(x^2+6)(2x+3)$ .

a)

$5x^2+12x+18$

b)

$2x^3+3x^2+12x+18$

c)

$3x^2+3x^2+12x+18$

d)

I don’t know 😓

9.

Expand ( x−3)².

a)

x² +6x+9

b)

x² −6x+9

c)

x² −6x−9

d)

x²− 9

10.

Expand (x +5)(x−5).

a)

x²−5

b)

x²+5

c)

x²+25

d)

x²−25

11.

Expand (2x + 3)².

a)

2x² +12x + 6

b)

2x² +12x + 9

c)

4x² +12x + 9

d)

4x² +12x + 6

12.

Expand (3x −½)(3x +½).

a)

9x² −½

b)

9x² −¼

c)

9x² + ½

d)

9x² +¼

13.

2(x + y + 2x) = ...

a)

6x + 2y

b)

6x - 2y

c)

6x + y

d)

6x - y

14.

Expand $\left(u^2-2\right)^3$

a)

$u^6-6u^4+12u^2-8$

b)

$u^6-16u^4+12u^2-8$

c)

$5u^6-20u^4+40u^2-40$

d)

$u^6-24u^4+12u^2-8$

15.

Expand $\left(4x-y\right)^3$

a)

$64x^3-48x^2y+12xy^2-y^3$

b)

$64x^3-16x^2y+4xy^2-y^3$

c)

$256x^3-96x^2y+16xy^2-y^3$

d)

$320x^3-160x^2y+40xy^2-5y^3$

16.

Expand: $\left(9a\ +\ 16\right)^2$

a)

$9a^2+16b^2+50ab$

b)

$9a^2+16b^2+576ab$

c)

$81a^2+256b^2+50ab$

d)

$81a^2+256b^2+576ab$

17.

Find the square of $\left(2a\ -\ 5b\right)$

a)

$4a^2+25b^2-20ab$

b)

$4a^2+25b^2+20ab$

c)

$4a^2-25b^2-20ab$

d)

$4a^2-25b^2+20ab$

18.

Expand $\left(\sqrt{3}a+\sqrt{5}n\right)^2$

a)

$\sqrt{3}a^2\ +\ \sqrt{5}n^2\ +2\sqrt{15}an$

b)

$3a^2+5n^2+2\sqrt{15}an$

c)

$9a^2+25n^2+30an$

19.

Expand $\left(\sqrt{3}a+\sqrt{5}n\right)^2$

a)

$\sqrt{3}a^2\ +\ \sqrt{5}n^2\ +2\sqrt{15}an$

b)

$3a^2+5n^2+2\sqrt{15}an$

c)

$9a^2+25n^2+30an$

20.

Fill in the blank: $\left(2x-\frac{3}{5x}\right)^2\ =\ 4x^2\ +\frac{9}{25x^2}-_{.......}$

a)

$\frac{5}{12}$

b)

$\frac{6}{5}$

c)

$\frac{6}{5x}$

d)

$\frac{12}{5}$

21.

Fill in the blank:
$\left(x\ -\ \frac{1}{x}\right)^2\ -\ \left(x+\frac{1}{x}\right)^2\ =$ ........

a)

2

b)

-2

c)

-4

d)

4

22.

Expand $\left(7-x-3y\right)^2$

a)

$49\ +x^2+9y^2\ -14x-6xy-42y$

b)

$49\ +\ x^2+9y^2\ -14x\ +\ 6xy\ -42y$

c)

$49+x^2+9y^2+14x-6xy+42y$

d)

$49+x^2+9y^2+14x+6xy+42y$

23.

If $\left(a+b+c\right)\ =\ 14\ and\ \left(a^2+b^2+c^2\right)=74,$ then find the value of $2\left(ab+bc+ca\right)$

a)

61

b)

270

c)

122

d)

135

24.

If $\left(a^2+b^2+c^2\right)=89$ and $\left(ab-bc-ca\right)=16$ are given, then value of which of the following expressions can be determined? (Tick all possible answers)

a)

(a+b-c)

b)

(-a-b+c)

c)

(a-b-c)

d)

(a+b+c)

25.

If $\left(x+\frac{1}{x}\right)=\frac{5}{2}$ , then find the value of $\left(x^3+\frac{1}{x^3}\right)\$ . (Consider ONLY positive value)

a)

$\frac{65}{8}$

b)

$\frac{185}{8}$

c)

$\frac{101}{8}$

d)

$\frac{55}{4}$

26.

If $\left(a+2b\right)=5$ , then fill in the blank in the following equation: $a^3+8b^3+.......\ =125$

a)

6ab

b)

3ab

c)

30ab

d)

15ab

27.

Expanded form of $\left(x+\frac{1}{3x}\right)^3$ is:

a)

$x^3+\frac{1}{x^3}+x+\frac{1}{3x}$

b)

$x^3+x+\frac{1}{3x}+\frac{1}{9x^2}$

c)

$x^3+x+\frac{1}{3x}+\frac{1}{27x^3}$

d)

$x^3+\frac{1}{27x^3}+\frac{x}{3}+\frac{3}{x}$

28.

Expand $\left(y-\frac{1}{y}\right)^3$ (Select ALL correct answers)

a)

$y^3-\frac{1}{y^3}-3y+\frac{3}{y}$

b)

$y^3-\frac{1}{y^3}-3y-\frac{3}{y}$

c)

$y^3-\frac{1}{y^3}-3\left(y-\frac{1}{y}\right)$

d)

$y^3-3y+\frac{3}{y}-\frac{1}{y^3}$

29.

$\left(a-b\right)^2=$

a)

$a^2-b^2$

b)

$a^2+b^2-2ab$

c)

$a^2+b^2+2ab$

d)

$2a-2b$

30.

$(a+b)^2+(a-b)^2=$

a)

$4ab$

b)

$a^2+b^2$

c)

$2\left(a^2+b^2\right)$

d)

$4\left(a^2+b^2\right)$

31.

$(a+b)^2-(a-b)^2=$

a)

$ab$

b)

$2ab$

c)

$3ab$

d)

$4ab$

32.

$(a+b)(a-b)^{ }=$

a)

$a^2b^2$

b)

$a^2-b^2$

c)

$2\left(a-b\right)$

d)

$a^2+b^2$

33.

$\left(a+\frac{1}{a}\right)^2=$

a)

$a^2+\frac{1}{a^2}^{ }$

b)

$a^2+\frac{1}{a^2}^{ }-2$

c)

$a^2+2+\frac{1}{a^2}^{ }$

d)

$2\left(a+\frac{1}{a}\right)$

34.

$\left(a-\frac{1}{a}\right)^2=$

a)

$a^2-\frac{1}{a^2}^{ }$

b)

$a^2+\frac{1}{a^2}^{ }-2$

c)

$a^2+\frac{1}{a^2}+2$

d)

$2\left(a-\frac{1}{a}\right)$

35.

$\left(a+\frac{1}{a}\right)^2+\left(a-\frac{1}{a}\right)^2=$

a)

$a^2+\frac{1}{a^2}$

b)

$2\left(a^2+\frac{1}{a^2}\right)$

c)

$3\left(a^2+\frac{1}{a^2}\right)$

d)

$4\left(a^2+\frac{1}{a^2}\right)$

36.

$\left(a+\frac{1}{a}\right)^2-\left(a-\frac{1}{a}\right)^2=$

a)

$1$

b)

$2$

c)

$3$

d)

$4$

37.

$\left(a+\frac{1}{a}\right)\left(a-\frac{1}{a}\right)=$

a)

$a^2-\frac{1}{a^2}$

b)

$a^2+\frac{1}{a^2}$

c)

$0$

d)

$None\ of\ these$

38.

$(x+a)(x+b)=$

a)

$x^2-(a+b)x+ab$

b)

$x^2+(a+b)x-ab$

c)

$x^2-(a+b)x-ab$

d)

$x^2+(a+b)x+ab$

39.

$(a+b)^3=$

a)

$a^3-b^3-3ab(a-b)$

b)

$a^3+b^3+3ab(a-b)$

c)

$a^3+b^3+3ab(a+b)$

d)

$a^3-b^3+3ab(a+b)$

40.

$(a-b)^3=$

a)

$a^3-b^3-3ab(a-b)$

b)

$a^3+b^3+3ab(a-b)$

c)

$a^3+b^3+3ab(a+b)$

d)

$a^3-b^3+3ab(a+b)$

41.

$(a+b)(a^2-ab+b^2)=$

a)

$a^3-b^3$

b)

$a^3+b^3$

c)

$a^3+b^3+3ab$

d)

$a^3-b^3-3ab$

42.

$(a-b)(a^2+ab+b^2)=$

a)

$a^3-b^3$

b)

$a^3+b^3$

c)

$a^3+b^3+3ab$

d)

$a^3-b^3-3ab$

43.

$(a+b+c)(a^2+b^2+c^2-ab-bc-ca)=$

a)

$a^3+b^3+c^3-abc$

b)

$a^3+b^3+c^3-2abc$

c)

$a^3+b^3+c^3+3abc$

d)

$a^3+b^3+c^3-3abc$

44.

$If\ \ a+b+c=0,\ then$

a)

$a^3+b^3+c^3=0$

b)

$a^3+b^3+c^3=abc$

c)

$a^3+b^3+c^3=2abc$

d)

$a^3+b^3+c^3=3abc$

45.

Find the product of (2x - 3y)(2x + 5y) using suitable identity.

a)

x²+ 4xy - 15xy

b)

2x²+ 4xy - 15xy

c)

x²- 15xy - 15xy

d)

2x²- 6xy - 15xy

46.

$\left(10a+12b\right)\left(10a-12b\right)=$

a)

$-100a^2-144b^2$

b)

$144b^2-100a^2$

c)

$100a^2+144b^2$

d)

$100a^2-144b^2$

47.

The simplified form of the expression (y² + 5)(y²- 3) is

a)

y⁴- 3y² - 15

b)

y⁴+ 2y² + 15

c)

y⁴- 3y² + 15

d)

y⁴+ 2y² - 15

48.

Simplify (a - b + c)(a + b + c)

a)

a²+ 2ab + b²- c²

b)

a²+ 2ac + c²- b²

c)

a²+ 2bc - c²- b²

d)

a²+ 2ac + c²- b²

49.

$\left(4a+2b\right)^2=$

a)

$16a^2+8ab-4b^2$

b)

$16a^2-8ab-4b^2$

c)

$16a^2-8ab+4b^2$

d)

$16a^2+8ab+4b^2$

50.

$\left(3t-4\right)^3$ Find the product:

a)

$27t^3-108t^2+144t-64$

b)

$9t^3-64$

c)

$9t^2-24t+16$

d)

$27t^3+108t^3-144t+64$

Expansions

Total questions: 50

Worksheet time: 31mins

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