因式分解：1.x^2+8xy-33y^22.(a+b)^2-3(a+b)-283.(x^2-2x)^2-11(x^2-2x)+244.a^3+2a^2b-9a-18b5.25a^2-5a-b^2-b6.1-a^2-b^2-2ab7.x^2-4xy+4y^2-4x+8y8.x^2-8xy+16y^2+2x-8y-3

Question

因式分解：1.x^2+8xy-33y^2 2.(a+b)^2-3(a+b)-28 3.(x^2-2x)^2-11(x^2-2x)+24 4.a^3+2a^2b-9a-18b
5.25a^2-5a-b^2-b 6.1-a^2-b^2-2ab 7.x^2-4xy+4y^2-4x+8y 8.x^2-8xy+16y^2+2x-8y-3

Answer 1

1.x^2+8xy-33y^2 =(x+11y)(x-3y) 2.(a+b)^2-3(a+b)-28 =(a+b-7)(a+b+4) 3.(x^2-2x)^2-11(x^2-2x)+24 =x^4-4x^3+4x^2-11x^2+22x+24 =x^4-4x^3-7x^2+22x+24 =x^4+x^3-5x^3-5x^2-2x^2-2x+24x+24 =x^3(x+1)-5x^2(x+1)-2x(x+1)+24(x+1) =(x+1)(x^3-5x^2-2x+24) 4.a^3+2a^2b-9a-18b=a^2(a+2b)-9(a+2b)=(a+2b)(a^2-9)=(a+2b)(a+3)(a-3) 5.25a^2-5a-b^2-b=(25a^2-b^2)-(5a+b)=(5a+b)(5a-b)-(5a+b)=(5a+b)(5a-b-1) 6.1-a^2-b^2-2ab=1-(a^2+b^2+2ab)=1-(a+b)^2=(1+a+b)(1-a-b) 7.x^2-4xy+4y^2-4x+8y=(x-2y)^2-4(x-2y)=(x-2y)(x-2y-4) 8.x^2-8xy+16y^2+2x-8y-3=(x-4y)^2+2(x-4y)-3=(x-4y+3)(x-4y-1)