Algebraic Expressions & Identities — Chapter Test | Class 8 IMO

Q1

(a + b)(a − b) equals ___ ?

Difference of squares: a² − b².

Q2

(a + b)² = a² + 2ab + ___ ?

(a + b)² = a² + 2ab + b².

Q3

Which identity gives x² − 9?

(x + 3)(x − 3) = x² − 9.

Q4

Combine like terms: 3x² + 2x².

3x² + 2x² = 5x².

Q5

Expand: 2x(x + 3).

2x × x + 2x × 3 = 2x² + 6x.

Q6

Expand: (x + 2)(x + 3).

x² + 5x + 6.

Q7

Expand: (x + 3)².

x² + 6x + 9.

Q8

Expand: (x − 4)².

x² − 8x + 16.

Q9

Expand: (x + 5)(x − 5).

x² − 25.

Q10

Expand: (x + 1)(x + 6).

x² + (1 + 6)x + 6 = x² + 7x + 6.

Q11

The area of a square of side (x + 2) is ___ ?

(x + 2)² = x² + 4x + 4.

Q12

Compute 103 × 97 using an identity.

(100 + 3)(100 − 3) = 10000 − 9 = 9991.

Q13

Compute 105² using an identity.

(100 + 5)² = 10000 + 1000 + 25 = 11025.

Q14

Simplify (a + b)² − (a − b)². If a = 3 and b = 2, what is the value?

(a + b)² − (a − b)² = 4ab = 4 × 3 × 2 = 24.