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\(a,a^2\left(a-b\right)+ab\left(a-c\right)=a\left(a+b\right)\left(a-c\right)\\ c,=\left(x^2-2x+1\right)\left(x^2+2x+1\right)=\left(x-1\right)^2\left(x+1\right)^2\\ b,=\left(x-5\right)^2-9y^2=\left(x-5-3y\right)\left(x-5+3y\right)\\ d,=4\left(x^2-9x+14\right)=4\left(x-7\right)\left(x-2\right)\)
\(a,15x-5xy\\ =5x\left(3-y\right)\\ b,\left(x^2+1\right)^2-4x^2\\ =\left(x^2-x+1\right)\left(x^2+x+1\right)\\ c,x^2-10x-9y^2+25\\ =\left(x-5\right)^2-9y^2\\ =\left(x-9y-5\right)\left(x+9y-5\right)\)
a) \(x^4+2x^3-4x-4=\left(x^4+2x^3+x^2\right)-\left(x^2+4x+4\right)\)
\(=\left(x^2+x\right)^2-\left(x+2\right)^2=\left(x^2+x-x-2\right)\left(x^2+x+x+2\right)\)
\(=\left(x^2-2\right)\left(x^2+2x+2\right)\)
a) Ta có: \(x^4+2x^3-4x-4\)
\(=\left(x^4+2x^3+x^2\right)-\left(x^2+4x+4\right)\)
\(=\left(x^2+x\right)^2-\left(x+2\right)^2\)
\(=\left(x^2+x-x-2\right)\left(x^2+x+x+2\right)\)
\(=\left(x^2-2\right)\cdot\left(x^2+2x+2\right)\)
a.
\(1-4x^2=\left(1-2x\right)\left(1+2x\right)\)
b.
\(8-27x^3=\left(2\right)^3-\left(3x\right)^3=\left(2-3x\right)\left(4+6x+9x^2\right)\)
c.
\(27+27x+9x^2+x^3=x^3+3.x^2.3+3.3^2.x+3^3\)
\(=\left(x+3\right)^3\)
d.
\(2x^3+4x^2+2x=2x\left(x^2+2x+1\right)=2x\left(x+1\right)^2\)
e.
\(x^2-y^2-5x+5y=\left(x-y\right)\left(x+y\right)-5\left(x-y\right)\)
\(=\left(x-y\right)\left(x+y-5\right)\)
f.
\(x^2-6x+9-y^2=\left(x-3\right)^2-y^2=\left(x-3-y\right)\left(x-3+y\right)\)
a) x² - 9
= x² - 3²
= (x - 3)(x + 3)
b) 4x² - 1
= (2x)² - 1²
= (2x - 1)(2x + 1)
c) x⁴ - 16
= (x²)² - 4²
= (x² - 4)(x² + 4)
= (x² - 2²)(x² + 4)
= (x - 2)(x + 2)(x + 4)
d) x² - 4x + 4
= x² - 2.x.2 + 2²
= (x - 2)²
e) x³ - 8
= x³ - 2³
= (x - 2)(x² + 2x + 4)
f) x³ + 3x² + 3x + 1
= x³ + 3.x².1 + 3.x.1² + 1³
= (x + 1)³
a) \(x^2-9+2\left(x+3\right)=\left(x-3\right)\left(x+3\right)+2\left(x+3\right)=\left(x+3\right)\left(x-3+2\right)=\left(x+3\right)\left(x-1\right)\)
b) \(x^2-10x+25-3\left(x-5\right)=\left(x-5\right)^2-3\left(x-5\right)=\left(x-5\right)\left(x-5-3\right)=\left(x-5\right)\left(x-8\right)\)
c) \(x^3-4x^2+3x=x\left(x^2-4x+3\right)=x\left(x-1\right)\left(x-3\right)\)
\(a,4x^2-4x+1\\ =\left(2x\right)^2-2.2x+1^2=\left(2x-1\right)^2\\ c,x^2-6xy-25z^2+9y^2\\ =\left(x^2-2.x.3y+9y^2\right)-\left(5z\right)^2\\ =\left(x-3y\right)^2-\left(5z\right)^2\\ =\left(x-3y-5z\right)\left(x-3y+5z\right)\)
Xem lại đề ý b
a: \(4x^2-x-5=\left(4x-5\right)\left(x+1\right)\)
b: \(x^2-2x-15=\left(x-5\right)\left(x+3\right)\)
b) \(x^2y-x^3-10y+10x\)
\(=x^2\left(y-x\right)-10\left(y-x\right)\)
\(=\left(y-x\right)\left(x^2-10\right)\)
c) \(x^2\left(x-2\right)+49\left(2-x\right)\)
\(=\left(x-2\right)\left(x^2-49\right)\)
\(=\left(x-2\right)\left(x-7\right)\left(x+7\right)\)
Bài 1: (2 điểm) Phân tích các đa thức sau thành nhân tử
a) a3 – a2c + a2b – abc
= a(a2 - ac + ab - bc)
= a[a(a - c) + b(a - c)]
= a(a - c)(a + b)
b) (x2 + 1)2 – 4x2
= (x2 + 1)2 – (2x)2
= (x2 + 1 - 2x)(x2 + 1 + 2x)
= (x - 1)2. (x + 1)2
c) x2 – 10x – 9y2 + 25
= (x2 - 10x + 25) - 9y2
= (x - 5)2 - (3y)2
= (x - 5 + 3y)(x - 5 - 3y)
d) 4x2 – 36x + 56
= 4x2 - 28x - 8x + 56
= (4x2 - 28x) - (8x - 56)
= 4x(x - 7) - 8(x - 7)
= (x - 7)(4x - 8)
= 4(x - 7)(x - 2)