(English Medium) ICSE Class 9 - CISCE Question Bank Solutions

Factorise the following:
(2a - b)² -9(3c - d)²

Factorise the following:
b² - 2bc + c² - a²

Factorise the following:

`x^2 + (1)/x^2 - 2`

Factorise the following:

(x² + y² – z²)² – 4x²y²

Factorise the following:

a² + b² – c² – d² + 2ab – 2cd

Factorise the following:
4xy - x² - 4y² + z²

Factorise the following:
4x² - 12ax - y² - z² - 2yz + 9a²

Factorise the following:
(x + y)³ - x - y

Factorise the following:
y⁴ + y² + 1

Factorise the following:

(a² – b²)(c² – d²) – 4abcd

Express each of the following as the difference of two squares:
(x² - 2x + 3)(x² + 2x + 3)

Express each of the following as the difference of two squares:
(x² - 2x + 3) (x² - 2x - 3)

Express each of the following as the difference of two squares:
(x² + 2x - 3) (x² - 2x + 3)

PQRS is a parallelogram. T is the mid-point of PQ and ST bisects ∠PSR.

Prove that: QR = QT

PQRS is a parallelogram. T is the mid-point of PQ and ST bisects ∠PSR.

Prove that: RT bisects angle R

PQRS is a parallelogram. T is the mid-point of PQ and ST bisects ∠PSR.

Prove that: ∠RTS = 90°

ABCD is a parallelogram. The bisector of ∠BAD meets DC at P, and AD is half of AB.

Prove that: BP bisects ∠ABC.

ABCD is a parallelogram. The bisector of ∠BAD meets DC at P, and AD is half of AB.

Prove that: ∠APB is a right angle.

In the given figure, MP is the bisector of ∠P and RN is the bisector of ∠R of parallelogram PQRS. Prove that PMRN is a parallelogram.

In a parallelogram ABCD, E is the midpoint of AB and DE bisects angle D. Prove that: BC = BE.