因式分解16x的四次方加81y的四次方-搜答案-拍题作业网

16x的16次方-y的四次方z的四次方=(4x^8-y^2z^2)(4x^8+y^2z^2)=(2x^4-yz)(2x^4+yz)(4x^8+2y^2z^2)

X^4-16Y^4=(X^2+4Y^2)(X^2-4Y^2)=(X^2+4Y^2)(X+2Y)(X-2Y)X^2-2XY+Y^2-2X+2Y+1=(X-Y)^2-2(X-y)+1=(X-Y-1)^2

x⁴-2y⁴-2x³y+xy³=(x+y)(x-2y)(x²-xy+y²)

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答：x的四次方-5x²y²-36的四次方=(x²)²-5x²y²-36(y²)²=(x²-9y²)(

x四次方y四次方-8x平方y平方+16=（x²y²-4）²=（xy+2）²（xy-2）²

2a的平方b+4ab-6b=2b(a^2+2a-3)=2b(a+3)(a-1)16x的四次方-8x的二次方y的二次方+y的四次方=(4x^2-y^2)^2=(2x+y)^2(2x-y)^2

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

x^4+y^4=x^4+2x^2y^2+y^4-2x^2y^2=(x^2+y^2)^2-2x^2y^2=(x^2+y^2+√2*xy)(x^2+y^2-√2*xy)

方法一：x^4＋y^4＋（x＋y）^4＝（x^4＋2x^2y^2＋y^4）－2x^2y^2＋（x^2＋2xy＋y^2）^2＝［（x^2＋y^2）^2－（xy）^2］＋［（x^2＋y^2＋2xy）^2－

x^4-13x^2y^2+36y^4=(x^2-4y^2)(x^2-9y^2)=(x+2y)(x-2y)(x+3y)(x-3y)

x的四次方-7x²y²-18y的四次方=(x^2-9y^2)(x^2+2y^2)=(x-3y)(x+3y)(x^2+2y^2)

1.x^4-16=(x^2+4)(x^2-4)=(x^2+4)(x+2)(x-2)2.x^2=(x+3)(x-3)3.16x^2-4y^2=4(4x^2-y^2)=4(2x+y)(2x-y)4.x^4

=(3x^2+4y^2)^2-9x^2y^2=(3x^2-3xy+4y^2)(3x^2+3xy+4y^2)

X四次方+X²Y²+X²Y²-X²Y²+Y四次方=（X²+Y²）²-X²Y²

令a=2x-y,b=2y-x,a+b=(2x-y)+(2y-x)=x+y(2x-y)四次方+(x+y)四次方+(2y-x)四次方=a四次方+(a+b)四次方+b四次方=(a+b)四次方+(a四次方+2

x的四次方-81x的平方y的平方=X2（x2-81Y2)=X2(X+9Y)(X-9Y)(字母后面的2代表平方）

x^4+2x+1=x^4-x²+x²+2x+1=x²(x-1)(x+1)+(x+1)²=(x+1)(x³-x²+x+1)

用因式除法可知,不能分解成x+1或者x-1的因式因此应分解成两个二项式相乘用待定系数法,设可分解成（x^2+ax-1)(X^2+bx-1),展开、归项后无解设可分解成（x^2+ax+1)(X^2+bx

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