因式分解 (1) (a+b)^2-4a^2 (2) (x^2+y^2)^2-4x^2y^2 (3) (p-4)(p+9)-5p(4) (2+2b-3c)^2-(a-2b+3c)^2这些题都怎做,谁能讲一讲?
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![因式分解 (1) (a+b)^2-4a^2 (2) (x^2+y^2)^2-4x^2y^2 (3) (p-4)(p+9)-5p(4) (2+2b-3c)^2-(a-2b+3c)^2这些题都怎做,谁能讲一讲?](/uploads/image/z/475937-17-7.jpg?t=%E5%9B%A0%E5%BC%8F%E5%88%86%E8%A7%A3+%281%29+%28a%2Bb%29%5E2-4a%5E2+%282%29+%28x%5E2%2By%5E2%29%5E2-4x%5E2y%5E2+%283%29+%28p-4%29%28p%2B9%29-5p%284%29+%282%2B2b-3c%29%5E2-%28a-2b%2B3c%29%5E2%E8%BF%99%E4%BA%9B%E9%A2%98%E9%83%BD%E6%80%8E%E5%81%9A%2C%E8%B0%81%E8%83%BD%E8%AE%B2%E4%B8%80%E8%AE%B2%3F)
因式分解 (1) (a+b)^2-4a^2 (2) (x^2+y^2)^2-4x^2y^2 (3) (p-4)(p+9)-5p(4) (2+2b-3c)^2-(a-2b+3c)^2这些题都怎做,谁能讲一讲?
因式分解 (1) (a+b)^2-4a^2 (2) (x^2+y^2)^2-4x^2y^2 (3) (p-4)(p+9)-5p
(4) (2+2b-3c)^2-(a-2b+3c)^2
这些题都怎做,谁能讲一讲?
因式分解 (1) (a+b)^2-4a^2 (2) (x^2+y^2)^2-4x^2y^2 (3) (p-4)(p+9)-5p(4) (2+2b-3c)^2-(a-2b+3c)^2这些题都怎做,谁能讲一讲?
(1) (a+b)^2-4a^2
=(a+b)^2-(2a)^2
=(a+b+2a)(a+b-2a)
=(3a+b)(b-a)
(2) (x^2+y^2)^2-4x^2y^2
=(x^2+y^2)^2-(2xy)^2
=(x^2+y^2+2xy)(x^2+y^2-2xy)
=(x+y)^2(x-y)^2
(3) (p-4)(p+9)-5p
=p^2-36
=(p+6)(p-6)
(4) (2+2b-3c)^2-(a-2b+3c)^2
=(2+2b-3c+1-2b+3c)(2+2b-3c-a+2b-3c)
=3(4b-3c-a+2)
其实以上四道题的解题过程中都含有平方差公式的知识,平方差公式:a^2-b^2=(a+b)(a-b),只要把它们变成平方差公式的形式,然后合并同类项就可以了.
套公式,整体带入
如:(a+b)^2=a^2+b^2+2ab
(x^2+y^2)^2-4x^2y^2=(x^2)^2+(y^2)^2+2(x^2)(y^2)+x^4+y^4+2x^2y^2-4x^2y^2
=(x^2-y^2)^2
其他也是套公式
(1) (a+b)^2-4a^2
=(a+b+2a)(a+b-2a)
=(3a+b)(b-a)
(2) (x^2+y^2)^2-4x^2y^2
=(x^2+2xy+y^2)(x^2-2xy+y^2)
=(x+y)^2(x-y)^2
(3) (p-4)(p+9)-5p
=p^2-36
=(p+6)(p-6)
(4) (2+2b-3c)^2-(a-2b+3c)^2
=(2+2b-3c+1-2b+3c)(2+2b-3c-a+2b-3c)
=3(4b-3c-a+2)
(1) (a+b)^2-4a^2=(a+b+2a)(a+b-2a)=(3a+b)(b-a)
(2) (x^2+y^2)^2-4x^2y^2=(x^2+2xy+y^2)(x^2-2xy+y^2)=(x+y)^2 * (x-y)^2
(3) (p-4)(p+9)-5p=p^2-36=(p+6)(p-6)
(4) (a+2b-3c)^2-(a-2b+3c)^2=(a+2b-3c+a-2b+3c)(a+2b-3c-a+2b-3c)
=(2a)*(4b-6c)=4a(2b-3c)
祝你进步啊!!