Question

simplify:
$(4 {x }^{2} - 9y {}^{2} ) ^{3} +( 9y { }^{2} - 16y {}^{2} ) {}^{3} + (16z {}^{2} - 4x {}^{2} ) {}^{3} \div (2x - 3y) {}^{3} + (3y - 4z) {}^{3} + (4z - 2x) {}^{3}$
​

Answer 1

Answer:

Its so long but i know the answer...

The answer is

$=\frac{-216x^4y^2+384x^4z^2+486x^2y^4-1536x^2z^4-351y^6+2048z^6}{4x^3-18x^2y+27xy^2-54y^2z+72yz^2-28z^3}$

Step-by-step explanation:

Solution=

$\frac{\left(4x^2-9y^2\right)^3+\left(9y^2-6y^2\right)^3+\left(16z^2-4x^2\right)^3}{\left(2x-3y\right)^3+\left(3y-4z\right)^3+\left(4z-2z\right)^3}$

$=\frac{\left(4x^2-9y^2\right)^3+\left(3y^2\right)^3+\left(16z^2-4x^2\right)^3}{\left(2x-3y\right)^3+\left(3y-4z\right)^3+\left(4z-2z\right)^3}$

$=\frac{\left(4x^2-9y^2\right)^3+\left(3y^2\right)^3+\left(16z^2-4x^2\right)^3}{\left(2x-3y\right)^3+\left(3y-4z\right)^3+\left(2z\right)^3}$

$=\frac{\left(4x^2-9y^2\right)^3+\left(3y^2\right)^3+\left(16z^2-4x^2\right)^3}{\left(2x-3y\right)^3+\left(3y-4z\right)^3+2^3z^3}$

$=\frac{\left(4x^2-9y^2\right)^3+27y^6+\left(16z^2-4x^2\right)^3}{\left(2x-3y\right)^3+\left(3y-4z\right)^3+8z^3}$

$=\frac{\left(4x^2-9y^2\right)^3+27y^6+\left(16z^2-4x^2\right)^3}{8x^3-36x^2y+54xy^2-108y^2z+144yz^2-56z^3}$

$=\frac{-432x^4y^2+768x^4z^2+972x^2y^4-3072x^2z^4-702y^6+4096z^6}{8x^3-36x^2y+54xy^2-108y^2z+144yz^2-56z^3}$

$=\frac{2\left(-216x^4y^2+384x^4z^2+486x^2y^4-1536x^2z^4-351y^6+2048z^6\right)}{8x^3-36x^2y+54xy^2-108y^2z+144yz^2-56z^3}$

$=\frac{-216x^4y^2+384x^4z^2+486x^2y^4-1536x^2z^4-351y^6+2048z^6}{\left(4x^3-18x^2y+27xy^2-54y^2z+72yz^2-28z^3\right)}$

$=\frac{-216x^4y^2+384x^4z^2+486x^2y^4-1536x^2z^4-351y^6+2048z^6}{4x^3-18x^2y+27xy^2-54y^2z+72yz^2-28z^3}$

Pls mark me as Brainliest I really worked hard for this question

I hope it helps :>