Factorize the following expression::
1) (x^2+4x+4)-9y^2
2) 25x^2-(9y^2-6y+1)
3) (x^2+6xy+9y^2)-16z^2
4) 4x^2-(4y^2-4yz+z^2)
F.2 factorize AR,,plz help
2007-10-24 4:31 am
回答 (2)
2007-10-24 5:18 am
✔ 最佳答案
1) (x^2+4x+4)-9y^2= (x + 2)^2 - (3y)^2
= [ (x + 2) - (3y) ][ (x + 2) + (3y) ]
= (x - 3y + 2)(x + 3y + 2)
2) 25x^2-(9y^2-6y+1)
= (5x)^2 - [ (3y)^2-6y+1 ]
= (5x)^2 - (3y - 1)^2
= [ (5x) - (3y - 1) ][ (5x) + (3y - 1) ]
= (5x - 3y + 1)(5x + 3y - 1)
3) (x^2+6xy+9y^2)-16z^2
= [ x^2+6xy+(3y)^2 ] - (4z)^2
= (x + 3y)^2 - (4z)^2
= [ (x + 3y) - (4z) ] [ (x + 3y) + (4z) ]
= (x + 3y - 4z)(x + 3y + 4z)
4) 4x^2-(4y^2-4yz+z^2)
= (2x)^2 - [ (2y)^2-4yz+z^2 ]
= (2x)^2 - (2y - z)^2
= [ (2x) - (2y - z) ][ (2x) + (2y - z) ]
= (2x - 2y + z)(2x + 2y - z)
2007-10-24 5:19 am
1.
(x^2 + 4x + 4) - 9y^2
= (x^2 + 2(x)(2) + 2^2) - (3y)^2
= (x + 2)^2 - (3y)^2
= (x + 3y + 2)(x - 3y + 2)
2.
25x^2 - (9y^2 - 6y + 1)
= (5x)^2 - ((3y)^2 - 2(3y)(1) + 1^2)
= (5x)^2 - (3y - 1)^2
= (5x + (3y - 1))(5x - (3y - 1))
= (5x + 3y - 1)(5x - 3y + 1)
3.
(x^2 + 6xy + 9y^2) - 16z^2
= (x^2 + 2(x)(3y) + (3y)^2) - (4z)^2
= (x + 3y)^2 - (4z)^2
= (x + 3y + 4z)(x + 3y - 4z)
4.
4x^2 - (4y^2 - 4yz + z^2)
= (2x)^2 - ((2y)^2 - 2(2y)(z) + z^2)
= (2x)^2 - (2y - z)^2
= (2x + (2y - z))(2x - (2y - z))
= (2x + 2y - z)(2x - 2y + z)
(x^2 + 4x + 4) - 9y^2
= (x^2 + 2(x)(2) + 2^2) - (3y)^2
= (x + 2)^2 - (3y)^2
= (x + 3y + 2)(x - 3y + 2)
2.
25x^2 - (9y^2 - 6y + 1)
= (5x)^2 - ((3y)^2 - 2(3y)(1) + 1^2)
= (5x)^2 - (3y - 1)^2
= (5x + (3y - 1))(5x - (3y - 1))
= (5x + 3y - 1)(5x - 3y + 1)
3.
(x^2 + 6xy + 9y^2) - 16z^2
= (x^2 + 2(x)(3y) + (3y)^2) - (4z)^2
= (x + 3y)^2 - (4z)^2
= (x + 3y + 4z)(x + 3y - 4z)
4.
4x^2 - (4y^2 - 4yz + z^2)
= (2x)^2 - ((2y)^2 - 2(2y)(z) + z^2)
= (2x)^2 - (2y - z)^2
= (2x + (2y - z))(2x - (2y - z))
= (2x + 2y - z)(2x - 2y + z)
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