2(5x + 10y)(2y – x)2 – 4(6y + 3x)(x – 2y)
Factorize
Answers
Answer:
How do you factor: 2 (5x+10y) (2y-x) ²-4 (6y+3x) (x-2y)?
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The first thing I would do is factor (-1) out of (x-2y)
(x - 2y) = -1 (2y - x)
Use this to slightly simplify the original expression:
2 (5x+10y) (2y-x)² - 4 (6y+3x) (x-2y)
2 (5x+10y) (2y-x)² + 4 (6y+3x) (2y-x)
Next, I would observe that (2y-x) is a factor of both terms
Factor (2y-x) out of both terms:
(2y - x) [ 2 (5x+10y)(2y-x) + 4 (6y+3x) ]
Next, I would rewrite every term so that they are in x±y order:
(x - 2y) [ 2 (5x + 10y) (x - 2y) + 4 ( 3x+6y)
Do you see what I see?
5x + 10y = 5 (x+2y)
3x + 6y = 3 (x+2y)
Factor (x+2y) out of both parts of the second term:
(x - 2y) [ 2 × 5 (x + 2y) (x - 2y) + 4 × 3 (x + 2y) ]
(x - 2y) (x + 2y) [ 2 × 5 (x - 2y) + 4 × 3 ]
(x - 2y) (x + 2y) [ 10 (x - 2y) + 12 ]
Expand the third term:
(x - 2y) (x + 2y) [ 10 (x - 2y) + 12 ]
(x - 2y) (x + 2y) ( 10x - ??y + ?? )
What did you get? (Did you remember to factor the 2 (greatest common factor) out of the third term?)