若x+y=-1,求x⁴+5x³y+x²y+8x²y²+xy²+5xy³+y⁴的值

若x+y=-1,求x⁴+5x³y+x²y+8x²y²+xy²+5xy³+y⁴的值
若x+y=-1,求x⁴+5x³y+x²y+8x²y²+xy²+5xy³+y⁴的值

若x+y=-1,求x⁴+5x³y+x²y+8x²y²+xy²+5xy³+y⁴的值
x⁴+5x³y+x²y+8x²y²+xy²+5xy³+y⁴
=x⁴+2x³y+x²y²+x²y²+2xy³+y⁴+3x³y+6x²y²+3xy³+x²y+xy²
=x²(x²+2xy+y²)+y²(x²+2xy+y²)+3xy(x²+2xy+y²)+xy(x+y)
=x²(x+y)²+y²(x+y)²+3xy(x+y)²+xy(x+y)
=x²+y²+3xy-xy
=x²+2xy+y²
=(x+y)²
=1