Using the formulas for factoring the sum and differences of cubes, factor each of the following:
PLEASE EXPLAIN UR ANSWERS IN STEPS!!!
2000 w^3 + 2y^3
5u^3-40(x+y)^3
2000 w^3+ 2y^3
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2000w^3+2y^3 [factor]
2(1000w^3+y^3) [factor the polynomial by following the cube law]
2(10w+y)(100w^2-10wy+y^2)
The law for factoring a^3+b^3 is:
(a+b)(a^2-ab+b^2)
5u^3-40(x+y)^3 [factor]
5(u^3-8(x+y)^3) [factor the polynomial by following another cube law]
5(u-2(x+y))(u^2+2u(x+y)+4(x+y)^2)
The law for factoring a^3-b^3 is:
(a-b)(a^2+ab+b^2)
Well the formula for factoring the sum of cubes is (A+B)(A^2-AB+B^2) and the formula for factoring the difference of cubes is
(A-B)(A^2+AB+B^2). Your first problem is a sum of cubes. A is 2000w and B is 2y so the factor would be (2000w+27)(2000w^2+2000w2y+2y^2). The second problem is a difference of cubes. Your A is 5u and your B is 40(x+y). Because of the ( ) we'll have to use [ ] as well. So to factor this, plug in the values of A and B into the formula. [5u-40(x+y)]{50u^2+[50u][40(x+y)]+[40(x+... The third one is the same as the first one.
the formula for sum of cubes x^3 + a^3 = (x + a)(x^2 - ax + a^2)
2000 w^3 + 2y^3 =
2(1000w^3 + y^3) = 2(10w + y)(100w^2 -10wy+y^2)
do the other one the same way, factor out 5 to start then use the difference of cubes formula.
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