分解因式:(1)25x²-16y² (2)(a-b)(x-y)-(b-a)(x+y) (3)a
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分解因式:(1)25x²-16y² (2)(a-b)(x-y)-(b-a)(x+y) (3)a²-4ab+4b²
(4)4+12(x-y)+9(x-y) (5)x³-9x (6)16x^4-1 (7)6xy²-9x²y-y³ (8)(2a-b)²+8ab
(4)4+12(x-y)+9(x-y) (5)x³-9x (6)16x^4-1 (7)6xy²-9x²y-y³ (8)(2a-b)²+8ab
(1)25x²-16y²=(5x+4y)*(5x-4y)
(2)(a-b)(x-y)-(b-a)(x+y)
=(a-b)[(x-y)+(x+y)]
=2x(a-b)
(3)a²-4ab+4b²=(a-2b)(a+2b)
4)4+12(x-y)+9(x-y)^2
=2^2+12(x-y)+[3(x-y)]^2
=[3(x-y)+2]^2
=(3x-3y+2)^2
(5)x³-9x =x(x^2-9) =x(x+3)(x-3)
(6)16x^4-1=(4x^2+1)(4x^2-1)=(4x^2+1)(2x+1)(2x-1)
(7)6xy²-9x²y-y³ =-y(y^2-6xy+9x^2)=-y(y-3x)^2
(8)(2a-b)²+8ab=4a^2+b^2-4ab+8ab
= 4a^2+b^2+4ab=(2a+b)^2
(2)(a-b)(x-y)-(b-a)(x+y)
=(a-b)[(x-y)+(x+y)]
=2x(a-b)
(3)a²-4ab+4b²=(a-2b)(a+2b)
4)4+12(x-y)+9(x-y)^2
=2^2+12(x-y)+[3(x-y)]^2
=[3(x-y)+2]^2
=(3x-3y+2)^2
(5)x³-9x =x(x^2-9) =x(x+3)(x-3)
(6)16x^4-1=(4x^2+1)(4x^2-1)=(4x^2+1)(2x+1)(2x-1)
(7)6xy²-9x²y-y³ =-y(y^2-6xy+9x^2)=-y(y-3x)^2
(8)(2a-b)²+8ab=4a^2+b^2-4ab+8ab
= 4a^2+b^2+4ab=(2a+b)^2
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