Answer:
[tex]64y^{18} - 1000z^{6} = (4y^{6} )^3 - (10z^2)^3[/tex] = [tex](4y^6 - 10z^2) (16y^{12} + 40y^6z^2 +100z^4)[/tex]
Step-by-step explanation:
The given expression is [tex]64y^{18} -1000z^{6}[/tex]
Here we can rewrite the given expression.
64 can be written as 4*4*4 = [tex]4^{3}[/tex]
[tex]y^{18} =( y^{6}) ^3[/tex] using the power of power rule of exponent.
So. [tex]64y^{18} = (4y^6)^{3}[/tex]
Now we can write 1000[tex]z^{6}[/tex] = [tex](10z^2)^3[/tex]
Therefore, [tex]64y^{18} - 1000z^{6} = (4y^{6} )^3 - (10z^2)^3[/tex]
This can be written as using the formula [tex](a - b)^3 = (a - b)(a^2 + ab + b^2)[/tex]
Here a = 4y^6 and b = 10z^2
= [tex](4y^6 - 10z^2) (16y^{12} + 40y^6z^2 +100z^4)[/tex]
