Question

Hasil pemfaktoran dari x⁴ - y⁴ adalah...
A. (x+y)²(x-y)²
B. (x²+y²)(x-y)²
C. (x²+y²)(x+y)(x-y)
D. (x+y)²(x+y)(x-y)

Answer 1

D.(x+y)² (x+y)(x-y)
karena (x+y)² itu x²+y² dan (x+y)(x-y) itu (x²-y²),
jadi (x²+y²) (x²-y²) = x⁴ - y⁴

Answer 2

A.
(x+y)² (x-y)²
= x² + 2xy + y² ( x² - 2xy + y²)
= x^4 -2x³y + x²y² - 4x²y² + 2xy³ + x²y² - 2x²y³ + y^4
Bukan

b.
(x²+y²)(x-y)²
= (x²+y²) (x²-2xy+y²)
= x^4 -2x³y + x²y² + x²y² -2xy³ + y^4
Bukan

c.
(x²+y²)(x+y)(x-y)
= (x³+x²y+xy²+y³)(x-y)
= x^4 - x³y + x³y - x²y² + x²y² - xy³ + xy³ - y^4
= x^4 - y^4
Benar.

Jadi, jawabannya c.