How to simplify the expression? And how to factor

1.) (-2x^3y^-4)(5x^-1y)


2.) Factor : 72x^3 - 711x^2 + 567

3.) Factor: x^3 - 64

OK. (-2x^3*y^-4)*(5x^-1*y). first multiply the constants to get -10.
then add the exponents on the x's +3 and -1 = +2.
then add the exponents on the y's -4 and +1 = -3.
So, your answer will be -10x^2*y^-3.

2. 72x^3 - 711x^2 + 567--you must be kidding....this one has 3 real roots and they are only approximate x = -0.85, x = 0.95 and and x = 9.8 and all of these are approximate




3. This is a classic case of the a^3-b^3 factorization.
The answer is (a-b)*(a^2 +ab + b^2) In this case b = 4 so the answer is
(x-4)*(x^2+4x+16).

1. -10x^2y^-3----->>> get the reciprocal of y to make the exponent positive

-10x^2/y^3

2. GCF is 9

9(8x^3 - 79x^2 + 63)

3. x^3 - 4^3

(x - 4) (x^2 + 4x + 16)

anything with a negative exponent move to the oppoitive place. so y^-4 become 1/y^4. If it was
1/y^-4 then you get y^4.

1. answer: -10x^2/y^3

3. x^3-4^3

(x-4)(x^2+4x+16)

3.) Factor: x^3 - 64 = x^3 - (4)^3 = (x-4)(x^2 +4x+16) ...............Ans
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