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a.
$x^2-y^2-2x+2y=(x^2-y^2)-(2x-2y)=(x-y)(x+y)-2(x-y)=(x-y)(x+y-2)$
b.
$x^2(x-1)+16(1-x)=x^2(x-1)-16(x-1)=(x-1)(x^2-16)=(x-1)(x-4)(x+4)$
c.
$x^2+4x-y^2+4=(x^2+4x+4)-y^2=(x+2)^2-y^2=(x+2-y)(x+2+y)$
d.
$x^3-3x^2-3x+1=(x^3+1)-(3x^2+3x)=(x+1)(x^2-x+1)-3x(x+1)$
$=(x+1)(x^2-4x+1)$
e.
$x^4+4y^4=(x^2)^2+(2y^2)^2+2.x^2.2y^2-4x^2y^2$
$=(x^2+2y^2)^2-(2xy)^2=(x^2+2y^2-2xy)(x^2+2y^2+2xy)$
f.
$x^4-13x^2+36=(x^4-4x^2)-(9x^2-36)$
$=x^2(x^2-4)-9(x^2-4)=(x^2-9)(x^2-4)=(x-3)(x+3)(x-2)(x+2)$
g.
$(x^2+x)^2+4x^2+4x-12=(x^2+x)^2+4(x^2+x)-12$
$=(x^2+x)^2-2(x^2+x)+6(x^2+x)-12$
$=(x^2+x)(x^2+x-2)+6(x^2+x-2)=(x^2+x-2)(x^2+x+6)$
$=[x(x-1)+2(x-1)](x^2+x+6)=(x-1)(x+2)(x^2+x+6)$
h.
$x^6+2x^5+x^4-2x^3-2x^2+1$
$=(x^6+2x^5+x^4)-(2x^3+2x^2)+1$
$=(x^3+x^2)^2-2(x^3+x^2)+1=(x^3+x^2-1)^2$
a) x2y+xy+x+1= (x2y+xy)+(x+1)=xy(x+10+(x+1)=(x+1)(xy+1)
b) x2-(a+b)x+ab=x2-ax-bx+ab=(x2-ax)-(bx-ab)=x(x-a)-b(x-a)=(x-a)(x-b)
c) ax2+ay-bx2-by=(ax2+ay)-(bx2+by)=a(x2+y)-b(x2+y)=(a-b)(x2+y)
d) ax-2x-a2+2a=(ax-2x)-(a2-2a)=x(a-2)-a(a-2)=(a-2)(x-a)
e) 2x2+4ax+x+2a=(2x2+4ax)+(x+2a)=2x(x+2a)+(x+2a)=(x+2a)(2x+1)
f) x3+ax2+x+a=(x3+ax2)+(x+a)=x2(x+a)+(x+a)=(x2+1)(x+a)
Bài 4
c) x(x - 2) + (x - 2)²
= (x - 2)(x + x - 2)
= (x - 2)(2x - 2)
= 2(x - 2)(x - 1)
d) 2x(x - y)² - 5(y - x)
= 2x(x - y)² + 5(x - y)
= (x - y)(2x + 5)
Bài 5
a) x² - 6x - 2xy + 12y
= (x² - 6x) - (2xy - 12y)
= x(x - 6) - y(x - 6)
= (x - 6)(x - y)
b) 10ax - 5ay - 2x + y
= (10ax - 5ay) - (2x - y)
= 5a(2x - y) - (2x - y)
= (2x - y)(5a - 1)
c) x⁴ + x³y - x - y
= (x⁴ + x³y) - (x + y)
= x³(x + y) - (x + y)
= (x + y)(x³ - 1)
= (x + y)(x - 1)(x² + x + 1)
d) x³ + 2x² - 4x - 8
= (x³ + 2x²) - (4x + 8)
= x²(x + 2) - 4(x + 2)
= (x + 2)(x² - 4)
= (x + 2)(x + 2)(x - 2)
= (x + 2)²(x - 2)
e) xy - 5x - y² + 5y
= (xy - 5x) - (y² - 5y)
= x(y - 5) - y(y - 5)
= (y - 5)(x - y)
f) ax - bx - 2cx - 2a + 2b + 4c
= (ax - bx - 2cx) - (2a - 2b - 4c)
= x(a - b - 2c) - 2(a - b - 2c)
= (a - b - 2c)(x - 2)
g) 5x²y + 5xy² - b²x - b²y
= (5x²y + 5xy²) - (b²x + b²y)
= 5xy(x + y) - b²(x + y)
= (x + y)(5xy - b²)
h) 4x³ - 4x² - 9x + 9
= (4x³ - 4x²) - (9x - 9)
= 4x²(x - 1) - 9(x - 1)
= (x - 1)(4x² - 9)
= (x - 1)(2x - 3)(2x + 3)
a: \(=x\left(x+y\right)-\left(x+y\right)=\left(x+y\right)\left(x-1\right)\)
b: \(=25-\left(x-2y\right)^2\)
\(=\left(5-x+2y\right)\left(5+x-2y\right)\)
a) x4+2x2+1=(x2+1)2
b)=3x2(a+b)+x(a+b)+5(a+b)=(a+b)(3x2+x+5)
c)=x2(a-b)-2x(a-b)-3(a-b)=(a-b)(x2-2x-3)=(a-b)(x-3)(x+1)
d)=2x(y2-a2)-5by(y+a)=(y+a)(2xy-2xa-5by)
\(\text{a) x}^4+2x^2+1=\left(x^2+1\right)^2\)
\(\text{b) 3}ax^2+3bx^2+ãx+bx+5a+5b=\left(3ax^2+3bx^2\right) +\left(ax+bx\right)+\left(5a+5b\right)=3x^2+x\left(a+b\right)+5\left(a+b\right)=\left(a+b\right)\left(3x^2+x+5\right)\)
\(\text{c) a}x^2-bx^2-2ax+2bx-3a+3b=\left(\text{a}x^2-bx^2\right)-\left(2ax-2bx\right)-\left(3a-3b\right)=x^2\left(a-b\right)-2x\left(a-b\right)-3\left(a-b\right)=\left(x^2-2x-3\right)\left(a-b\right)\)
Bài 3:
\(B=x^4-4x^3-2x^2+12x+9=\left(x^4+x^3\right)-\left(5x^3+5x^2\right)+\left(3x^2+3x\right)+\left(9x+9\right)=\left(x^3-5x^2+3x+9\right)\left(x+1\right)=\left[\left(x^3+x^2\right)-\left(6x^2+6x\right)+\left(9x+9\right)\right]\left(x+1\right)=\left(x^2-6x+9\right)\left(x+1\right)^2=\left(x-3\right)^2\left(x+1\right)^2=\left[\left(x-3\right)\left(x+1\right)\right]^2\)
Bài 3:
\(B=x^4-4x^3-2x^2+12x+9\)
\(=x^4-3x^3-x^3+3x^2-5x^2+15x-3x+9\)
\(=\left(x-3\right)\left(x^3-x^2-5x-3\right)\)
\(=\left(x-3\right)\left(x^3-3x^2+2x^2-6x+x-3\right)\)
\(=\left(x-3\right)^2\cdot\left(x+1\right)^2\)
\(=\left(x^2-2x-3\right)^2\)
a) \(x^2-2x-4y^2-4y=\left(x^2-4y^2\right)-\left(2x+4y\right)=\left(x-2y\right)\left(x+2y\right)-2\left(x+2y\right)=\left(x+2y\right)\left(x-2y-2\right)\)
b) \(x^3+2x^2+2x+1=\left(x+1\right)\left(x^2-x+1\right)+2x\left(x+1\right)=\left(x+1\right)\left(x^2-x+1+2x\right)=\left(x+1\right)\left(x^2+x+1\right)\)
c) \(x^3-4x^2+12x-27=x^3-3x^2-x^2+3x+9x-27=x^2\left(x-3\right)-x\left(x-3\right)+9\left(x-3\right)=\left(x-3\right)\left(x^2-x+9\right)\)
d) \(a^6-a^4+2a^3+2a^2=a^2\left(a^4-a^2+2a+2\right)=a^2\left[a^2\left(a-1\right)\left(a+1\right)+2\left(a+1\right)\right]=a^2\left(a+1\right)\left(a^3-a^2+2\right)=a^2\left(a+1\right)\left[a^3+a^2-2a^2+2\right]=a^2\left(a+1\right)\left[a^2\left(a+1\right)-2\left(a-1\right)\left(a+1\right)\right]=a^2\left(a+1\right)^2\left(a^2-2a+2\right)\)
a) Ta có: \(x^2-2x-4y^2-4y\)
\(=\left(x^2-4y^2\right)-\left(2x+4y\right)\)
\(=\left(x-2y\right)\left(x+2y\right)-2\left(x+2y\right)\)
\(=\left(x+2y\right)\left(x-2y-2\right)\)
b) Ta có: \(x^3+2x^2+2x+1\)
\(=\left(x^3+1\right)+2x\left(x+1\right)\)
\(=\left(x+1\right)\left(x^2-x+1\right)+2x\left(x+1\right)\)
\(=\left(x+1\right)\left(x^2+x+1\right)\)
c) Ta có: \(C=4x^2+y^2-4xy+8x-4y+4\)
\(=\left(2x-y\right)^2+2\cdot\left(2x-y\right)\cdot2+2^2\)
\(=\left(2x-y+2\right)^2\)
Cho mình xin đáp án câu a và b được không?