【搜题】十字相乘的因式分解题目!

2个回答

  • 练习

    把下列各式分解因式:

    1.x4-15x2+26; 2.(x+y) 2-(x+y)-2;

    3.y4-26y2+25; 4.(a-b) 2+6(b-a)+5;

    5.(x2-2x)2-7(x2-2x)-8; 6.x2-2xy-8y2;

    7.x2+(a+b)x+ab; 8.x4-7x2y2+6y4;

    答案:

    1.(x2-13)(x2-2); 2.(x+y+1)(x+y-2);

    3.(y+5)(y-5)(y+1)(y-1); 4.(a-b-1)(a-b-5);

    5.(x-4)(x+2)(x-1) 2; 6.(x+2y)(x-4y);

    7.(x+a)(x+b); 8.(x+y)(x-y)(x2-6y2);

    小结

    把下列各式分解因式:

    1.(1)x4+7x2-18; (2)x6+8x3+15;

    (3)m2x2-8mx+12; (4)x2y2-7xy+10;

    2.(1)x2-7xy+12y2; (2)a2+2ab-15b2;

    (3)m2+4mn-12n2; (4)p2+9pq+18q2.

    3.(1)(m+n) 2-(m+n)-30; (2)(x-y) 2-3(x-y)-40;

    (3)(2m+n) 2-4r(2m+n)+3r2; (4)(a-b) 2-12(a-b)-45.

    4.(1)(x2-4x) 2-(x2-4x)-20; (2)(a2+5a+3)(a2+5a-2)-6.

    答案:

    1.(1)(x2-2)(x2+9); (2)(x2+3)(x3+5);

    (3)(mx-2)(mx-6); (4)(xy-2)(xy-5).

    2.(1)(x-3y)(x-4y); (2)(a+5b)(a-3b);

    (3)(m-2n)(m+6n); (4)(p+3q)(p+6q).

    3.(1)(m+n-6)(m+n+5); (2)(x-y+5)(x-y-8);

    (3)(2m+n-r)(2m+n-3r); (4)(a-b-15)(a-b+3).

    4.(1)(x+1)(x-5)(x-2) 2;

    (2) (a2+5a+3)(a2+5a-4)-6

    =[(a2+5a)+3][(a2+5a)-2]-6

    =(a2+5a) 2+(a2+5a)-12

    =(a2+5a+4)(a2+5a-3)

    =(a+1)(a+4))(a2+5a-3).

    可以吗?