Question

初一因式分解：①4x²-y²+4x+1 ②（x+2）（x+4）+1 ③x的四次方-3x²-4

Answer 1

：①4x²-y²+4x+1
=4x²+4x+1-y²
=（2x+1)^2-y^2
=(2x+1+y)(2x+1-y)
②（x+2）（x+4）+1
=x^2+6x+8+1
=x^2+6x+9
=(x+3)^2
③x的四次方-3x²-4
=(x^2-4)(x^2+1)
=(x+2)(x-2)(x^2+1)

追问

麻烦了，再问道，计算(2x+3y)²(2x-3y)²

追答

(2x+3y)²(2x-3y)²
=[(2x+3y)(2x-3y)]^2
=(4x^2-9y^2)^2
=16x^4-72x^2y^2+81y^4

Answer 2

①4x²+4x+1-y²=（2x+1）²-y²=（2x+1+y）（2x+1-y）
②x²+6x+8+1=（x+3）²
③（x²+1）（x²-4）=（x²+1）（x+2)(x-2)
手打不容易，随时追问！

Answer 3

4x²-y²+4x+1
=(2x+1)²-y²
=(2x+y+1)(2x-y+1)

（x+2）（x+4）+1
=x²+6x+9
=(x+3)²

x^4-3x²-4

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

(2x+3y)²(2x-3y)²

=[(2x+3y)(2x-3y)]²
=[4x²-9y²]²
=16x^4-72x²y²+81y^4