Factorize
$\displaystyle
= y^6-125 = (y^3)^2 - (5)^3
$
can i factorize it more? thanksss
Hello, jvignacio
Factorize: .$\displaystyle y^6-125$
$\displaystyle (y^3)^2 - (5)^3$ . . . . This is not factored!
For example -- Factor: .$\displaystyle 6x + 21$
"Factor" means to express it as a product of two or more expressins.
. . Answer: .$\displaystyle 3 \times (2x + 7)$
This is not factored: .$\displaystyle (2)(3)(x) + (3)(7)$
Certainly, parts of it are factored, but it is still a sum of two expressions.
We have: .$\displaystyle y^6 - 125 \;=\;(y^2)^3 - (5)^3$ . . . difference of cubes!
. . You are expected to know that: .$\displaystyle a^3 -b^3 \:=\:(a-b)(a^2 + ab +b^2)$
Therefore: . $\displaystyle (y^2)^3 - (5)^3 \;=\;(y^2 - 5)(y^4 + 5y^2 + 25)$