Question

分解因式①(X+Y)²-16（X-Y）² ②（X+Y+Z）²-（X-Y-Z）²

Answer 1

①(X+Y)²-16（X-Y）²
=（x+y+4x-4y）（x+y-4x+4y）
=(5x-3y)(-3x+5y)

②（X+Y+Z）²-（X-Y-Z）²
=(x+y+z+x-y-z)(x+y+z-x+y+z)
=2x(2y+2z)
=4x(y+z)

提示：运用平方差公式

Answer 2

①(X+Y)²-16（X-Y）²
=(X+Y+4X-4Y)(X+Y-4X+4Y)
=(5X-3Y)(-3X+5Y)

②（X+Y+Z）²-（X-Y-Z）²
=（X+Y+Z+X-Y-Z)(X+Y+Z-X+Y+Z)
=2X(2Y+2Z)
=4X(Y+Z)

Answer 3

(1)(X+Y)²-16（X-Y）²
=(X+Y+4X-4Y)(X+Y-4X+4Y)
=(5X-3Y)(-3X+5Y)

(2)(x+y+z)²-(x-y-z)²
=〔x+y+z+(x-y-z)〕〔x+y+z-(x-y-z)〕
=4x(y+z)

Answer 4

①(X+Y)²-16（X-Y）² =(X+Y)²-（4X-4Y）² =(X+Y+4X-4Y)(X+Y-4X+4Y)=(5X-3Y)(-3X+5Y)
②（X+Y+Z）²-（X-Y-Z）² =(X+Y+Z+X-Y-Z)(X+Y+Z-X+Y+Z)=2X(2Y+2Z)=4X(Y+Z)