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 Read More »
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
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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
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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
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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 –
Factorize : a^3 – 3a^2b + 3ab^2 – b^3 + 8 Read More »
Factorize 8x^3 + 27y^3 + 36x^2y + 54xy^2 Factorize : \( 8x^3 + 27y^3 + 36x^2y + 54xy^2 \) \[ 8x^3 + 27y^3 + 36x^2y + 54xy^2 \] \[ = 8x^3 + 36x^2y + 54xy^2 + 27y^3 \] \[ = (2x)^3 + 3(2x)^2(3y) + 3(2x)(3y)^2 + (3y)^3 \] \[ = (2x + 3y)^3 \] Next
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Factorize 8/27x^3 + 1 + 4/3x^2 + 2x Factorize : \( \frac{8}{27}x^3 + 1 + \frac{4}{3}x^2 + 2x \) \[ \frac{8}{27}x^3 + 1 + \frac{4}{3}x^2 + 2x \] \[ = \frac{8}{27}x^3 + \frac{4}{3}x^2 + 2x + 1 \] \[ = \left(\frac{2x}{3}\right)^3 + 3\left(\frac{2x}{3}\right)^2(1) + 3\left(\frac{2x}{3}\right)(1)^2 + 1^3 \] \[ = \left(\frac{2x}{3} + 1\right)^3 \] Next
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Factorize 125x^3 – 27y^3 – 255x^2y + 135xy^2 Factorize : \( 125x^3 – 27y^3 – 255x^2y + 135xy^2 \) \[ 125x^3 – 27y^3 – 255x^2y + 135xy^2 \] \[ = 125x^3 – 255x^2y + 135xy^2 – 27y^3 \] \[ = (5x)^3 – 3(5x)^2(3y) + 3(5x)(3y)^2 – (3y)^3 \] \[ = (5x – 3y)^3 \] Next
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Factorize 64a^3 + 125b^3 + 240a^2b + 300ab^2 Factorize : \( 64a^3 + 125b^3 + 240a^2b + 300ab^2 \) \[ 64a^3 + 125b^3 + 240a^2b + 300ab^2 \] \[ = 64a^3 + 240a^2b + 300ab^2 + 125b^3 \] \[ = (4a)^3 + 3(4a)^2(5b) + 3(4a)(5b)^2 + (5b)^3 \] \[ = (4a + 5b)^3 \] Next
Factorize : 64a^3 + 125b^3 + 240a^2b + 300ab^2 Read More »
Simplify (2x – 5y)³ – (2x + 5y)³ Simplify : \((2x – 5y)^3 – (2x + 5y)^3\) \[ (2x – 5y)^3 – (2x + 5y)^3 \] \[ = \left[(2x – 5y) – (2x + 5y)\right] \left[(2x – 5y)^2 + (2x – 5y)(2x + 5y) + (2x + 5y)^2\right] \] \[ = (-10y) \left[(4x^2 – 20xy
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