Free Printable Algebraic identities

1.

Expand (4x − 5)(4x + 5).

a)

4x² − 25

b)

4x² + 25

c)

16x² + 25

d)

16x² − 25

2.

(x² - y²) × (x² + y²) = ______

a)

2x² + 2y²

b)

x⁴ - y⁴

c)

x⁴ + y⁴

d)

2x⁴

3.

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

4.

$Expansion\ of\ \left(x\ +4\right)^2\ is\$

a)

$x^2+8x+16$

b)

x $x^2+8x+4$

c)

$x^2-8x+16$

d)

$x^2+8x-16$

5.

(x - 8) ( x - 8) = ______

a)

x² - 64

b)

x² + 64

c)

x²- 16x + 64

d)

x² + 16x + 64

6.

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

a)

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

b)

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

c)

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

d)

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

7.

$25a^2-4b^2$ is of the form

a)

$a^2-b^2$

b)

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

c)

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

d)

none of these

8.

(5-p)(5-p) is of the form

a)

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

b)

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

c)

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

d)

none of these

9.

$\left(3x+5y\right)\left(3x+5y\right)$ is of the form

a)

$3x^2-5y^2$

b)

$\left(3x-5y\right)^2$

c)

$\left(3x+5y\right)^2$

d)

none of these

10.

$\left(a-5\right)\left(2a-9\right)$ is of the form

a)

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

b)

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

c)

$\left(x+a\right)\left(x+b\right)$

d)

none of these

11.

(p - q)²

a)

p² + 2pq + q²

b)

p² + 2pq - q²

c)

p² - 2pq - q²

d)

p² - 2pq + q²

12.

Expand (x−4)².

a)

x² −8x+16

b)

x² −8x−16

c)

x² +8x+16

d)

x² −16

13.

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

a)

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

b)

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

c)

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

d)

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

14.

Expand (2x + 1)².

a)

4x² +4x +1

b)

4x² +1

c)

4x² +2x +1

d)

4x² +4x +2

15.

Expand (3x − 2)².

a)

3x² − 12x − 4

b)

3x² − 12x + 4

c)

9x² − 12x + 4

d)

9x² − 12x − 4

16.

What will be the area of a rectangle if its length is 4a²b and breadth 3ab?

a)

12a²b

b)

12a³b

c)

7a³b

d)

12a³b²

17.

Subtract: -6x²y from -10x²y

a)

4x²y

b)

-4x²y

c)

16x²y

d)

-16x²y

18.

Can the following expression be a monomial (xyz + a) where 'a' is any whole number

a)

For a = 1

b)

For a = -1

c)

For a = 0

d)

Not possible

19.

The expression (l + m) (2m + p) − 2m (p + m) can be simplified as

a)

2lm + lp

b)

2lm + lp − 2mp

c)

2lm + lp + mp

d)

2lm + lp − mp

20.

What is the product of (x² − y²) and (3x + 2y)?

a)

3x³ − 2y³ + 3x²y + 3xy²

b)

3x³ + 2y³ - 2x²y − 3xy²

c)

3x³ − 2y³ + 2x²y − 3xy²

d)

3x³ − 3y³ + 2x²y − 3xy²

21.

Which of the following expressions is equivalent to the expression 945 × 855?

a)

900² − 45²

b)

900² + 45²

c)

900² + (45 + 55) 900 + (45 × 55)

d)

800² + (45 + 55) 800 + 45 × 55

22.

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

23.

The degree of the polynomial: 4x²y + x² - 2y² is ______

a)

2

b)

3

c)

4

d)

-2

24.

(x² - y²) × (x² + y²) = ______

a)

2x² + 2y²

b)

x⁴ - y⁴

c)

x⁴ + y⁴

d)

2x⁴

25.

(x - 8) ( x - 8) = ______

a)

x² - 64

b)

x² + 64

c)

x²- 16x + 64

d)

x² + 16x + 64

26.

What kind of expression is xyz?

a)

Monomial

b)

Binomial

c)

Trinomial

d)

None of the above

27.

(x - 8) ( x - 8) = ______

a)

x² - 64

b)

x² + 64

c)

x²- 16x + 64

d)

x² + 16x + 64

28.

Expand (4x − 5)(4x + 5).

a)

4x² − 25

b)

4x² + 25

c)

16x² + 25

d)

16x² − 25

29.

Expand (x−4)².

a)

x² −8x+16

b)

x² −8x−16

c)

x² +8x+16

d)

x² −16

30.

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

a)

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

b)

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

c)

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

d)

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

31.

(x² - y²) × (x² + y²) = ______

a)

2x² + 2y²

b)

x⁴ - y⁴

c)

x⁴ + y⁴

d)

2x⁴

32.

(99)^3

(a)

33.

(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)

34.

(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)

35.

$Expansion\ of\ \left(x\ +4\right)^2\ is\$

a)

$x^2+8x+16$

b)

x $x^2+8x+4$

c)

$x^2-8x+16$

d)

$x^2+8x-16$

36.

(x - 8) ( x - 8) = ______

a)

x² - 64

b)

x² + 64

c)

x²- 16x + 64

d)

x² + 16x + 64

37.

Expand (4x − 5)(4x + 5).

a)

4x² − 25

b)

4x² + 25

c)

16x² + 25

d)

16x² − 25

38.

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

a)

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

b)

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

c)

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

d)

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

39.

Expand (4x − 5)(4x + 5).

a)

4x² − 25

b)

4x² + 25

c)

16x² + 25

d)

16x² − 25

40.

The identity (y + a) (y +b) is

a)

y² + ( a - b )y + ab

b)

y² - ( a + b )y + ab

c)

y² + ( a + b )y - ab

d)

y² + ( a + b )y + ab

41.

The product of (a+b) and (a-b) is

a)

a²+b²

b)

a²-b²

c)

ab+bc

d)

none of these

42.

(m+1)(m+3) is of the form

a)

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

b)

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

c)

$\left(x+a\right)\left(x+b\right)$

d)

none of these

43.

$25a^2-4b^2$ is of the form

a)

$a^2-b^2$

b)

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

c)

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

d)

none of these

44.

(5-p)(5-p) is of the form

a)

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

b)

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

c)

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

d)

none of these

45.

$\left(3x+5y\right)\left(3x+5y\right)$ is of the form

a)

$3x^2-5y^2$

b)

$\left(3x-5y\right)^2$

c)

$\left(3x+5y\right)^2$

d)

none of these

46.

$\left(a-5\right)\left(2a-9\right)$ is of the form

a)

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

b)

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

c)

$\left(x+a\right)\left(x+b\right)$

d)

none of these

47.

$\left(4-a\right)\left(4-b\ \right)$ is of the form

a)

$\left(x+a\right)\left(x+b\right)$

b)

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

c)

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

d)

none of these

48.

$\left(a^2+2ab\ +b^2\right)$ is the expansion of

a)

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

b)

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

c)

$\left(a+b\right)^3$

d)

none of these

49.

(p - q)²

a)

p² + 2pq + q²

b)

p² + 2pq - q²

c)

p² - 2pq - q²

d)

p² - 2pq + q²

50.

(x + a)(x + b) =

a)

x² + abx + ab

b)

x² + ax - bx + ab

c)

2x + (a+b)x + ab

d)

x² + (a+b)x + ab

51.

Expand (x−4)².

a)

x² −8x+16

b)

x² −8x−16

c)

x² +8x+16

d)

x² −16

52.

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

a)

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

b)

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

c)

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

d)

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

53.

Expand (2x + 1)².

a)

4x² +4x +1

b)

4x² +1

c)

4x² +2x +1

d)

4x² +4x +2

54.

Expand (3x − 2)².

a)

3x² − 12x − 4

b)

3x² − 12x + 4

c)

9x² − 12x + 4

d)

9x² − 12x − 4

55.

(x² - y²) × (x² + y²) = ______

a)

2x² + 2y²

b)

x⁴ - y⁴

c)

x⁴ + y⁴

d)

2x⁴

56.

(x - 8) ( x - 8) = ______

a)

x² - 64

b)

x² + 64

c)

x²- 16x + 64

d)

x² + 16x + 64

57.

Expand (4x − 5)(4x + 5).

a)

4x² − 25

b)

4x² + 25

c)

16x² + 25

d)

16x² − 25

58.

Expand (x−4)².

a)

x² −8x+16

b)

x² −8x−16

c)

x² +8x+16

d)

x² −16

59.

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

a)

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

b)

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

c)

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

d)

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

60.

Using identity find 201 x 199

a)

3000

b)

3999

c)

39999

d)

31111

61.

Find 87² - 13²

a)

7200

b)

7300

c)

7400

d)

7500

62.

$\left(a^2+2ab\ +b^2\right)$ is the expansion of

a)

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

b)

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

c)

$\left(a+b\right)^3$

d)

none of these

63.

(p - q)²

a)

p² + 2pq + q²

b)

p² + 2pq - q²

c)

p² - 2pq - q²

d)

p² - 2pq + q²

64.

(5-p)(5-p) is of the form

a)

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

b)

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

c)

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

d)

none of these

65.

The product of 93x99 is

a)

9207

b)

9000

c)

8250

d)

8976

66.

Find (102)² - (98)²

a)

200

b)

400

c)

600

d)

800

67.

Find 96 X 104, using identity

a)

9984

b)

9974

c)

9964

d)

9954

68.

Expand (x−4)².

a)

x² −8x+16

b)

x² −8x−16

c)

x² +8x+16

d)

x² −16

69.

Expand (x−4)².

a)

x² −8x+16

b)

x² −8x−16

c)

x² +8x+16

d)

x² −16

70.

The square of x² - 2y²is ______

a)

x⁴ - 4x²y²+ 4y⁴

b)

x⁴ + 4x²y²+ 4y⁴

c)

x⁴ - 4x²y²- 4y⁴

d)

None of the above

71.

(7a+5b)^2

a)

49a^2+25b^2+35ab

b)

49a^2+25b^2+12ab

c)

49a^2+25b^2+70ab

d)

49a^2+25b^2+2ab

72.

(6b+5a)(6a-5a)

a)

12b^2-10a^2

b)

36b^2-25a^2

c)

24b^2-25a^2

d)

36b^2-25b^2

73.

(5x+8)^2

a)

25x^2+64+40x

b)

25x^2+64+80x

c)

5x^2+64+40x

d)

5x^2+64+80x

74.

(x+4)(x+6)

a)

x^2+10x+24

b)

x^2+2x+2

c)

x^2+2x+10

d)

x^2+10x+10

75.

(x+3)(x-4)

a)

x^2+x+12

b)

x^2+x-12

c)

x^2-x+12

d)

x^2-x-12

76.

(45x-5y)(45x+5y)

(a)

77.

(x−5)(x−6)

a)

x^2-11-30

b)

x^2-11+30

c)

x^2+11-30

d)

x^2+11+30

78.

(7x-3y)^2

a)

49x^2-42xy+9y^2

b)

49x^2-21xy+9y^2

c)

7x^2-21xy+3y^2

d)

7x^2-42xy+9y^2

79.

(5x+7y)^2

a)

5x^2+70xy+49y^2

b)

25x^2+70xy+49y^2

c)

25x^2+35xy+49y^2

d)

5x^2+70xy+7y^2

80.

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

a)

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

b)

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

c)

$x+\frac{1}{x}-2$

d)

$x-\frac{1}{x}+2$

81.

201 x 199

a)

3000

b)

3999

c)

31111

d)

39999

82.

1+1 (From Shaurya message he said: this is a break, but if u get it first i feel bad)

a)

2

b)

window

c)

11

d)

all of the above

Algebraic identities

Total questions: 82

Worksheet time: 3hrs 26mins

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