Educational

Factorize 27x^3 – y^3 – z^3 – 9xyz Factorize the following expression : \( 27x^3 – y^3 – z^3 – 9xyz \) \[ 27x^3 – y^3 – z^3 – 9xyz \] \[ = (3x)^3 + (-y)^3 + (-z)^3 – 3(3x)(-y)(-z) \] \[ = \left[(3x) + (-y) + (-z)\right] \left[ (3x)^2 + (-y)^2 + (-z)^2 – […]

Factorize x^3 – 8y^3 + 27z^3 + 18xyz Factorize the following expression : \( x^3 – 8y^3 + 27z^3 + 18xyz \) \[ x^3 – 8y^3 + 27z^3 + 18xyz \] \[ = x^3 + (-2y)^3 + (3z)^3 – 3(x)(-2y)(3z) \] \[ = \left[x + (-2y) + 3z\right] \left[ x^2 + 4y^2 + 9z^2 +

Factorize a^3 + 8b^3 + 64c^3 – 24abc Factorize the following expression : \( a^3 + 8b^3 + 64c^3 – 24abc \) \[ a^3 + 8b^3 + 64c^3 – 24abc \] \[ = a^3 + (2b)^3 + (4c)^3 – 3(a)(2b)(4c) \] \[ = (a + 2b + 4c) \left( a^2 + 4b^2 + 16c^2 –

Factorize a^3x^3 – 3a^2bx^2 + 3ab^2x – b^3 Factorize : \( a^3x^3 – 3a^2bx^2 + 3ab^2x – b^3 \) \[ a^3x^3 – 3a^2bx^2 + 3ab^2x – b^3 \] \[ = (ax)^3 – 3(ax)^2(b) + 3(ax)(b)^2 – b^3 \] \[ = (ax – b)^3 \] Next Question / Full Exercise

Factorize x^3 – 12x(x – 4) – 64 Factorize : \( x^3 – 12x(x – 4) – 64 \) \[ x^3 – 12x(x – 4) – 64 \] \[ = x^3 – 12x^2 + 48x – 64 \] \[ = x^3 – 3x^2(4) + 3x(4)^2 – 4^3 \] \[ = (x – 4)^3 \] Next

Factorize 8a^3 – 27b^3 – 36a^2b + 54ab^2 Factorize : \( 8a^3 – 27b^3 – 36a^2b + 54ab^2 \) \[ 8a^3 – 27b^3 – 36a^2b + 54ab^2 \] \[ = 8a^3 – 36a^2b + 54ab^2 – 27b^3 \] \[ = (2a)^3 – 3(2a)^2(3b) + 3(2a)(3b)^2 – (3b)^3 \] \[ = (2a – 3b)^3 \] Next

Factorize 8a^3 + 27b^3 + 36a^2b + 54ab^2 Factorize : \( 8a^3 + 27b^3 + 36a^2b + 54ab^2 \) \[ 8a^3 + 27b^3 + 36a^2b + 54ab^2 \] \[ = 8a^3 + 36a^2b + 54ab^2 + 27b^3 \] \[ = (2a)^3 + 3(2a)^2(3b) + 3(2a)(3b)^2 + (3b)^3 \] \[ = (2a + 3b)^3 \] Next

Factorize 8x^3 + y^3 + 12x^2y + 6xy^2 Factorize : \( 8x^3 + y^3 + 12x^2y + 6xy^2 \) \[ 8x^3 + y^3 + 12x^2y + 6xy^2 \] \[ = (2x)^3 + 3(2x)^2(y) + 3(2x)(y)^2 + y^3 \] \[ = (2x + y)^3 \] Next Question / Full Exercise

Factorize x^3 + 8y^3 + 6x^2y + 12xy^2 Factorize : \( x^3 + 8y^3 + 6x^2y + 12xy^2 \) \[ x^3 + 8y^3 + 6x^2y + 12xy^2 \] \[ = x^3 + 6x^2y + 12xy^2 + 8y^3 \] \[ = x^3 + 3x^2(2y) + 3x(2y)^2 + (2y)^3 \] \[ = (x + 2y)^3 \] Next

Factorize a^3 – 3a^2b + 3ab^2 – b^3 + 8 Factorize : \( a^3 – 3a^2b + 3ab^2 – b^3 + 8 \) \[ a^3 – 3a^2b + 3ab^2 – b^3 + 8 \] \[ = (a – b)^3 + 2^3 \] \[ = (a – b + 2) \left[(a – b)^2 – 2(a –