Secondary School (English Medium) (5 to 8) Class 8 - CBSE Question Bank Solutions for Mathematics

Factorise the following using the identity a² – b² = (a + b)(a – b).

8a³ – 2a

Factorise the following using the identity a² – b² = (a + b)(a – b).

`x^2 - y^2/100`

Factorise the following using the identity a² – b² = (a + b)(a – b).

9x² – (3y + z)²

Factorise the expression and divide them as directed:

(x² – 22x + 117) ÷ (x – 13)

Factorise the expression and divide them as directed:

(x³ + x² – 132x) ÷ x(x – 11)

Factorise the expression and divide them as directed:

(2x³ – 12x² + 16x) ÷ (x – 2)(x – 4)

Factorise the expression and divide them as directed:

(9x² – 4) ÷ (3x + 2)

Factorise the expression and divide them as directed:

(3x² – 48) ÷ (x – 4)

Factorise the expression and divide them as directed:

(x⁴ – 16) ÷ x³ + 2x² + 4x + 8

Factorise the expression and divide them as directed:

(3x⁴ – 1875) ÷ (3x² – 75)

The sum of first n natural numbers is given by the expression `n^2/2 + n/2`. Factorise this expression.

The sum of (x + 5) observations is x⁴ – 625. Find the mean of the observations.

The base of a parallelogram is (2x + 3 units) and the corresponding height is (2x – 3 units). Find the area of the parallelogram in terms of x. What will be the area of parallelogram of x = 30 units?

The radius of a circle is 7ab – 7bc – 14ac. Find the circumference of the circle. `(pi = 22/7)`

Verify the following:

(ab + bc)(ab – bc) + (bc + ca)(bc – ca) + (ca + ab)(ca – ab) = 0

Verify the following:

(a + b + c)(a² + b² + c² – ab – bc – ca) = a³ + b³ + c³ – 3abc

Verify the following:

(p – q)(p² + pq + q²) = p³ – q³

Verify the following:

(m + n)(m² – mn + n²) = m³ + n³

Verify the following:

(a² – b²)(a² + b²) + (b² – c²)(b² + c²) + (c² – a²) + (c² + a²) = 0

Verify the following:

`((3p)/7 + 7/(6p))^2 - (3/7p  + 7/(6p))^2 = 2`