Question

因式分解 过程

①3X-12X³②-4x³+16x²-26x③m³-m④x²+x-2⑤x的16次方-y16次方
化简求值：①（a²-b²）÷（a+b)+（a²-2ab+b²）÷（a-b)其中a=½ ， b=-2
②已知a+b=2，ab=2 求½a³b+a²b²+½ab²的值

Answer 1

①3X-12X³
=3x(1-4x²)
=3x(1+2x)(1-2x)

②-4x³+16x²-26x
=-2x(2x²-8x+13)

③m³-m
=m(m²-1)
=m(m-1)(m+1)

④x²+x-2
=(x-1)(x+2)

⑤x的16次方-y16次方

=(x^8+y^8)(x^8-y^8)
=(x^8+y^8)(x^4+y^4)(x^4-y^4)
=(x^8+y^8)(x^4+y^4)(x²+y²)(x²-y²)
=(x^8+y^8)(x^4+y^4)(x²+y²)(x+y)(x-y)

化简求值：①（a²-b²）÷（a+b)+（a²-2ab+b²）÷（a-b)其中a=½ ， b=-2
(a²-b²)÷(a+b)+(a²-2ab+b²)÷(a-b)
=(a+b)(a-b)÷(a+b)+(a-b)²÷(a-b)
=(a-b)+(a-b)
=2a-2b
其中a=1/2,b=-2
原式=2*1/2+2*2
=1+4
=5

②已知a+b=2，ab=2 求½a³b+a²b²+½ab²的值
½a³b+a²b²+½ab²
=1/2ab(a²+2ab+b²)
=1/2ab(a+b)²
因为a+b=2 ab=2
原式=1/2*2*4
=4

Answer 2

①3X-12X³
=3x(1-4x²)
=3x(1-2x)(1+2x)

②-4x³+16x²-26x
=-2x(2x²-8x+13)

③m³-m
=m(m²-1)
=m(m-1)(m+1)

④x²+x-2
=(x-1)(x+2)

⑤x的16次方-y16次方
=(x^8+y^8)(x^8-y^8)
=(x^8+y^8)(x^4+y^4)
=(x^8+y^8)(x^4+y^4)(x²+y²)(x+y)(x-y)

化简求值：
①（a²-b²）÷（a+b)+（a²-2ab+b²）÷（a-b)其中a=½ ， b=-2
=(a-b)(a+b)÷(a+b)+(a-b)²÷(a-b)
=a-b+a-b
=2a-2b
=2*1/2-2*(-2)
=1+4
=5

②已知a+b=2，ab=2 求½a³b+a²b²+½ab³的值
½a³b+a²b²+½ab³
=1/2ab(a²+2ab+b²)
=1/2ab(a+b)²
=1/2*2*2²
=4