Question

计算：①2m²-m(2m-5n)-n(5m-n)②(3x-y)²-(3x+y)²-2xy③(m+1)(m+2)(m-1)(m-2)

④(x+1)²(x²+1)²(x-1)²
因式分解：①3分之4x²y³-9分之2x³y ②(x²+4)²-16x² ③16x的四次方-8x²y²+y的四次方 ④-5a³+5a

速度速度，好的加悬赏！

Answer 1

①2m²-m(2m-5n)-n(5m-n)
=2m²-2m²+5mn-5mn+n²
=n²
.
②(3x-y)²-(3x+y)²-2xy
=9x²-6xy+y²-(9x²+6xy+y²)-2xy
=-6xy-6xy-2xy
=-14xy
.
③(m+1)(m+2)(m-1)(m-2)
=(m+1)(m-1)(m+2)(m-2)
=(m²-1)(m²-4)
=m的4次幂 - 5m² +4
.
④(x+1)²(x²+1)²(x-1)²
=(x+1)²(x-1)²(x²+1)²
=(x²-1)²(x²+1)²
= (x的4次幂-1)²
=x的8次幂 - 2*x的4次幂 +1
.
因式分解：
① 3分之4x²y³-9分之2x³y
=9分之2*x²y*(6y²- x²)
=9分之2*x²y*(根号6*y +x) (根号6*y -x)
.
②(x²+4)²-16x²
=[(x²+4)+4x]²[(x²+4)-4x]²
=(x²+4x+4)²(x²-4x+4)²
=(x+2)的4次幂*(x-2)的4次幂
.
③16x的四次方-8x²y²+y的四次方
=(4x²-y²)²
=(2x+y)²(2x-y)²
.
④-5a³+5a=-5a(a²-1)=-5a(a+1)(a-1)