Question

Which expression is equivalent to 64y18-1000z6

Answer 1

64y^18 -1000z^6 = (4y^6)^3 -(10z^2)^3

Answer 2

Answer:

$64y^{18} - 1000z^{6} = (4y^{6} )^3 - (10z^2)^3$ =  $(4y^6 - 10z^2) (16y^{12} + 40y^6z^2 +100z^4)$

Step-by-step explanation:

The given expression is $64y^{18} -1000z^{6}$

Here we can rewrite the given expression.

64 can be written as 4*4*4 = $4^{3}$

$y^{18} =( y^{6}) ^3$ using the power of power rule of exponent.

So. $64y^{18} = (4y^6)^{3}$

Now we can write 1000$z^{6}$ = $(10z^2)^3$

Therefore, $64y^{18} - 1000z^{6} = (4y^{6} )^3 - (10z^2)^3$

This can be written as using the formula $(a - b)^3 = (a - b)(a^2 + ab + b^2)$

Here a = 4y^6 and b = 10z^2

= $(4y^6 - 10z^2) (16y^{12} + 40y^6z^2 +100z^4)$