May 2026

Factorize (x – 2y)^3 + (2y – 3z)^3 + (3z – x)^3 Factorize the following expression : \( (x – 2y)^3 + (2y – 3z)^3 + (3z – x)^3 \) \[ (x – 2y)^3 + (2y – 3z)^3 + (3z – x)^3 \] \[ \text{Let } a = (x – 2y),\quad b = (2y – […]

Factorize (a – 3b)^3 + (3b – c)^3 + (c – a)^3 Factorize the following expression : \( (a – 3b)^3 + (3b – c)^3 + (c – a)^3 \) \[ (a – 3b)^3 + (3b – c)^3 + (c – a)^3 \] \[ \text{Let } x = (a – 3b),\quad y = (3b –

Factorize (2x – 3y)^3 + (4z – 2x)^3 + (3y – 4z)^3 Factorize the following expression : \( (2x – 3y)^3 + (4z – 2x)^3 + (3y – 4z)^3 \) \[ (2x – 3y)^3 + (4z – 2x)^3 + (3y – 4z)^3 \] \[ \text{Let } a = (2x – 3y),\quad b = (4z –

Factorize (3x – 2y)^3 + (2y – 4z)^3 + (4z – 3x)^3 Factorize the following expression : \( (3x – 2y)^3 + (2y – 4z)^3 + (4z – 3x)^3 \) \[ (3x – 2y)^3 + (2y – 4z)^3 + (4z – 3x)^3 \] \[ \text{Let } a = (3x – 2y),\quad b = (2y –

Find the Value of 48^3 – 30^3 – 18^3 Without actually computing the cubes, find the value of : \( 48^3 – 30^3 – 18^3 \) \[ 48^3 – 30^3 – 18^3 \] \[ = 48^3 + (-30)^3 + (-18)^3 \] \[ \text{Since } 48 + (-30) + (-18) = 0 \] \[ \therefore a^3

Factorize 2√2a^3 + 16√2b^3 + c^3 – 12abc Factorize the following expression : \( 2\sqrt{2}a^3 + 16\sqrt{2}b^3 + c^3 – 12abc \) \[ 2\sqrt{2}a^3 + 16\sqrt{2}b^3 + c^3 – 12abc \] \[ = (\sqrt{2}a)^3 + (2\sqrt{2}b)^3 + c^3 – 3(\sqrt{2}a)(2\sqrt{2}b)(c) \] \[ = (\sqrt{2}a + 2\sqrt{2}b + c) \] \[ \times \left[ 2a^2 + 8b^2

Factorize 3√3a^3 – b^3 – 5√5c^3 – 3√15abc Factorize the following expression : \( 3\sqrt{3}a^3 – b^3 – 5\sqrt{5}c^3 – 3\sqrt{15}abc \) \[ 3\sqrt{3}a^3 – b^3 – 5\sqrt{5}c^3 – 3\sqrt{15}abc \] \[ = (\sqrt{3}a)^3 + (-b)^3 + (-\sqrt{5}c)^3 – 3(\sqrt{3}a)(-b)(-\sqrt{5}c) \] \[ = (\sqrt{3}a – b – \sqrt{5}c) \] \[ \times \left[ 3a^2 + b^2

Factorize 2√2a^3 + 3√3b^3 + c^3 – 3√6abc Factorize the following expression : \( 2\sqrt{2}a^3 + 3\sqrt{3}b^3 + c^3 – 3\sqrt{6}abc \) \[ 2\sqrt{2}a^3 + 3\sqrt{3}b^3 + c^3 – 3\sqrt{6}abc \] \[ = (\sqrt{2}a)^3 + (\sqrt{3}b)^3 + c^3 – 3(\sqrt{2}a)(\sqrt{3}b)(c) \] \[ = (\sqrt{2}a + \sqrt{3}b + c) \] \[ \times \left[ 2a^2 + 3b^2

Factorize 2√2a^3 + 3√3b^3 + c^3 – 3√6abc Factorize the following expression : \( 2\sqrt{2}a^3 + 3\sqrt{3}b^3 + c^3 – 3\sqrt{6}abc \) \[ 2\sqrt{2}a^3 + 3\sqrt{3}b^3 + c^3 – 3\sqrt{6}abc \] \[ = (\sqrt{2}a)^3 + (\sqrt{3}b)^3 + c^3 – 3(\sqrt{2}a)(\sqrt{3}b)(c) \] \[ = (\sqrt{2}a + \sqrt{3}b + c) \] \[ \times \left[ 2a^2 + 3b^2

Multiply (4x^2 + y^2 + 9z^2 + 2xy + 3yz – 6xz) by (2x – y + 3z) Multiply : \( (4x^2 + y^2 + 9z^2 + 2xy + 3yz – 6xz) \) by \( (2x – y + 3z) \) \[ (4x^2 + y^2 + 9z^2 + 2xy + 3yz – 6xz)(2x – y