Multiply (x^2 + 4y^2 + z^2 + 2xy + xz – 2yz) by (x – 2y – z) Multiply : \( (x^2 + 4y^2 + z^2 + 2xy + xz – 2yz) \) by \( (x – 2y – z) \) \[ (x^2 + 4y^2 + z^2 + 2xy + xz – 2yz)(x – 2y […]

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

Factorize 8x^3 – 125y^3 + 180xy + 216 Factorize the following expression : \( 8x^3 – 125y^3 + 180xy + 216 \) \[ 8x^3 – 125y^3 + 180xy + 216 \] \[ = (2x)^3 + (-5y)^3 + 6^3 – 3(2x)(-5y)(6) \] \[ = (2x – 5y + 6) \left[ 4x^2 + 25y^2 + 36 +

Factorize 125 + 8x^3 – 27y^3 + 90xy Factorize the following expression : \( 125 + 8x^3 – 27y^3 + 90xy \) \[ 125 + 8x^3 – 27y^3 + 90xy \] \[ = 5^3 + (2x)^3 + (-3y)^3 – 3(5)(2x)(-3y) \] \[ = (5 + 2x – 3y) \left[ 25 + 4x^2 + 9y^2 –

Factorize 1/27x^3 – y^3 + 125z^3 + 5xyz Factorize the following expression : \( \frac{1}{27}x^3 – y^3 + 125z^3 + 5xyz \) \[ \frac{1}{27}x^3 – y^3 + 125z^3 + 5xyz \] \[ = \left(\frac{x}{3}\right)^3 + (-y)^3 + (5z)^3 – 3\left(\frac{x}{3}\right)(-y)(5z) \] \[ = \left(\frac{x}{3} – y + 5z\right) \left[ \frac{x^2}{9} + y^2 + 25z^2 +

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