Answer:
a) Factoring 12xy - 24x^4y^2:
12xy - 24x^4y^2 = 12xy(1 - 2x^3y)
b) Factoring 2xy - 12x^5y^2 + 8x^2y^3:
2xy - 12x^5y^2 + 8x^2y^3 = 2xy(1 - 6x^4y + 4x^2y^2)
c) Factoring 4xy + 2wy - 10x^2 - 5wx:
4xy + 2wy - 10x^2 - 5wx = (2y - 5x)(2x + w)
Therefore, the factored forms are:
a) 12xy(1 - 2x^3y)
b) 2xy(1 - 6x^4y + 4x^2y^2)
c) (2y - 5x)(2x + w)
Explanation:
a) To factor 12xy - 24x^4y^2, we can factor out the greatest common factor (GCF) of the terms, which in this case is 12xy:
12xy - 24x^4y^2 = 12xy(1 - 2x^3y)
b) To factor 2xy - 12x^5y^2 + 8x^2y^3, we can first factor out the GCF of the terms, which is 2xy:
2xy - 12x^5y^2 + 8x^2y^3 = 2xy(1 - 6x^4y + 4x^2y^2)
c) To factor 4xy + 2wy - 10x^2 - 5wx, we can group the terms:
(4xy + 2wy) - (10x^2 + 5wx)
Now, let's factor out the GCF from each group separately:
4xy + 2wy = 2y(2x + w)
10x^2 + 5wx = 5x(2x + w)
Combining the factors, we have:
2y(2x + w) - 5x(2x + w)
Now, we can factor out the common factor (2x + w):
(2x + w)(2y - 5x)
Therefore, the factored form of 4xy + 2wy - 10x^2 - 5wx is (2x + w)(2y - 5x).