16. Factorize 5xy + 90qy — 30y2
— 15xq
A. (15y + 5q)(x — 6y)
B. (5y — 15q)(x + 6y)
C. (5y — q) (15x — 6y)
D. (5y — 15q)(x — 6y)
D. (5y — 15q)(x — 6y)
To factorize the expression 5xy + 90qy - 30y^2 - 15xq, we can rearrange the terms to group them together:
5xy - 15xq + 90qy - 30y^2.
Now, let's factor out the common factors from each group separately:
5xy - 15xq = 5x(y - 3q),
90qy - 30y^2 = 30y(3q - y).
Combining these factorizations, we have:
5xy + 90qy - 30y^2 - 15xq = 5x(y - 3q) + 30y(3q - y).
Simplifying further, we get:
5xy + 90qy - 30y^2 - 15xq = 5x(y - 3q) - 30y(y - 3q).
Now, we can factor out the common factor (y - 3q) from both terms:
5x(y - 3q) - 30y(y - 3q) = (y - 3q)(5x - 30y).
Therefore, the factorized form of the given expression is (y - 3q)(5x - 30y).
Comparing this with the answer choices, we can see that the correct option is:
D. (5y - 15q)(x - 6y).