Question

因式分解(2x+y)的四次方-(x+2y)的四次方？

Answer 1

(2x +y)⁴ - (x + 2y)⁴
= [(2x + y)² - (x + 2y)²][(2x + y)² + (x + 2y)²]
= [(2x + y) - (x + 2y)][(2x + y) + (x + 2y)][(2x + y)² + (x + 2y)²]
= (x - y)(3x + 3y)(5x² + 8xy + 5y²)
= 3(x - y)(x + y)(5x² + 8xy + 5y²)

Answer 2

(2x+y)^4-(x+2y)^4

=[(2x+y)²]²-[(x+2y)²]²

=[(2x+y)²+(x+2y)²]·[(2x+y)²-(x+2y)²]

=[(4x²+4xy+y²)+(x²+4xy+4y²)]·[(2x+y)+(x+2y)]·[(2x+y)-(x+2y)]

=(5x²+8xy+5y²)·(3x+3y)·(x-y)

=3(x+y)(x-y)(5x²+8xy+5y²)