1.Phân tích các đa thức sau thành nhân tử:
a, \(x^2+6x+9\)
b, \(10x-25-x^2\)
c, \(8x^3-\dfrac{1}{8}\)
d, \(\dfrac{1}{25}x^2-64y^2\)
2.Phân tích các đa thức sau thành nhân tử:
a, \(x^3_{ }+\dfrac{1}{27}\)
b, \(\left(a+b\right)^3-\left(a-b\right)^3\)
c, \(\left(a+b\right)^3+\left(a-b\right)^3\)
d, \(8x^3+12x^2y+6xy^2+y^3\)
e, \(-x^3+9x^2-27x+27\)
3.Tìm \(x\),biết:
a, \(2-25x^2=0\)
b, \(x^2-x+\dfrac{1}{4}=0\)
Bài giải:
1.
a) x2 + 6x + 9 = x2 + 2 . x . 3 + 32 = (x + 3)2
b) 10x – 25 – x2 = -(-10x + 25 +x2) = -(25 – 10x + x2)
= -(52 – 2 . 5 . x – x2) = -(5 – x)2
c) 8x3 - 1818 = (2x)3 – (1212)3 = (2x - 1212)[(2x)2 + 2x . 1212 + (1212)2]
= (2x - 1212)(4x2 + x + 1414)
d) 125125x2 – 64y2 = (15x)2(15x)2- (8y)2 = (1515x + 8y)(1515x - 8y)
2.
a) x3 + 127 = x3 + (13)3 = (x + 13)(x2 – x . 13+ (13)2)
=(x + 13)(x2 – 13x + 19)
b) (a + b)3 – (a - b)3
= [(a + b) – (a – b)][(a + b)2 + (a + b) . (a – b) + (a – b)2]
= (a + b – a + b)(a2 + 2ab + b2 + a2 – b2 + a2 – 2ab + b2)
= 2b . (3a3 + b2)
c) (a + b)3 + (a – b)3 = [(a + b) + (a – b)][(a + b)2 – (a + b)(a – b) + (a – b)2]
= (a + b + a – b)(a2 + 2ab + b2 – a2 +b2 + a2 – 2ab + b2]
= 2a . (a2 + 3b2)
d) 8x3 + 12x2y + 6xy2 + y3 = (2x)3 + 3 . (2x)2 . y +3 . 2x . y + y3 = (2x + y)3
e) - x3 + 9x2 – 27x + 27 = 27 – 27x + 9x2 – x3 = 33 – 3 . 32 . x + 3 . 3 . x2 – x3 = (3 – x)3
