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Factor the following polynomial completely.?
Factor the following polynomial completely.
-x2y2 + x4 + 4y2 - 4x2
a. (x - 2)(x - 2)(x + y)(x - y)
b. (x + 2)(x + 2)(x + y)(x - y)
c. (x + 2)(x - 2)(x + y)(x - y)
3 Answers
- Jun AgrudaLv 71 decade agoFavorite Answer
1st factor (x²):
= - x²y² + x⁴ + 4y² - 4x²
= x⁴ - 4x² + - x²y² + 4y²
= x²(x² - 4) - y²(x² - 4)
= (x² - y²)(x² - 4)
= (x + y)(x - y)(x + 2)(x - 2)
Answer: c. (x + 2)(x - 2)(x + y)(x - y)
- Anonymous1 decade ago
-x2y2 + x4 + 4y2 - 4x2
Rearrange the formula
-x2y2 + 4y2 + x4 - 4x2
Group and Factor
(-x2y2 + 4y2) (+ x4 - 4x2)
= -y^2 (x^2-4) + x^2 (x^2 - 4)
= (x^2 - y^2) (x^2 - 4)
= (x + y)(x - y)(x + 2)(x-2)
The Correct answer is C
- BrianLv 51 decade ago
-x2y2 + x4 + 4y2 - 4x2
x^2(x^2 - 4) - y^2(x^2 - 4)
x^2(x + 2)(x - 2) - y^2(x + 2)(x - 2)
(x + 2)(x - 2) [ x^2 - y^2 ]
(x + 2)(x - 2)(x - y)(x + y)
Answer is C; (x + 2)(x - 2)(x + y)(x - y)
