1)
a) x2 - 9+ ( x-3) d) 3x2-7x-10
e) 5x3-5x2y-10x2+10xy
b) x3-4x2+4x-xy2 f) 3x3-6xy+3y2-12z2
c) x3-4x2+12x-27
1. Phân tích thành nhân tử
a) x2 + 7x + 10; b) x2 – 21x + 110; c) 3x2 + 12x + 9; d) 2ax2 - 16ax + 30a.
2. Phân tích thành nhân tử
a) x2 + x – 6; b) x2 – 2x – 15; c) 4x2 - 12x - 160; d) 5x2y - 10xy - 15y.
3. Phân tích thành nhân tử
a) x2 – xy – 20y2 ; b) 3x4 + 6x2y2 – 45y4 ; c) 2bx2 – 4bxy - 70y2
4. Giải phương trình
a) x2 + x = 72; b) 3x2 – 6x = 24 c) 5x3 – 10x2 = 120x.
5. Phân tích thành nhân tử
a) 3x2 -11x + 6; b) 8x2 + 10x – 3 ; c) 8x2 -2x -1 .
bài 2 phân tích đa thức sau thành nhân tử
a ) -x - y2 + x2 - y b) x(x+y) -5x - 5y
c) 5x3 - 5x2y - 10x2 + 10xy e) 27x3 - 8y3
d) x2 - y2 - 2xy + y2
\(a,=\left(x-y\right)\left(x+y\right)-\left(x+y\right)=\left(x+y\right)\left(x-y-1\right)\\ b,=\left(x+y\right)\left(x-5\right)\\ c,=5x^2\left(x-y\right)-10x\left(x-y\right)=5x\left(x-2y\right)\left(x-y\right)\\ d,=x^2-2xy=x\left(x-2y\right)\\ e,=\left(3x-2y\right)\left(9x^2+6xy+4y^2\right)\)
Bài 1. Làm tính nhân:
a) 3x2 (2 - 5xy)
b) -\(\dfrac{2}{3}\) xy (xy2 - x3 + 4)
c) ( x - 7 y )( xy + 1)
Bài 2. Rút gọn các biểu thức sau:
a) 5x(4x2 - 2x +1) - 2x(10x2 - 5x - 2)
b) 3x( x - 2) - 5x(1- x) - 8(x2 - 3)
d) (x3 - 2x)(x2 +1)
Bài 1:
\(a,6x^2-15x^3y\\ b,=-\dfrac{2}{3}x^2y^3+\dfrac{2}{3}x^4y-\dfrac{8}{3}xy\)
Bài 2:
\(a,=20x^3-10x^2+5x-20x^3+10x^2+4x=9x\\ b,=3x^2-6x-5x+5x^2-8x^2+24=24-11x\\ c,=x^5+x^3-2x^3-2x=x^5-x^3-2x\)
câu d của bài 2 là của bài 1 nha mình để nhầm chỗ huhu
A=5x3-7x2-(-3x3+4x2)+(x2-x3+5x-1)
B=(3x2+5x3-7x4)-(5x3-4x2+x4-3)
\(A=5x^3-7x^2+3x^3-4x^2+x^2-x^3+5x-1=7x^3-10x^2+5x-1\)
\(B=5x^3+3x^2-7x^4-5x^3+4x^2-x^4+3=-8x^4+7x^2+3\)
\(A=7x^3-10x^2+5x-1\)
\(B=-8x^4+7x^2+3\)
Bài 1: Làm tính nhân:
a) 2x. (x2 – 7x -3) b) ( -2x3 + y2 -7xy). 4xy2
c)(-5x3). (2x2+3x-5) d) (2x2 - xy+ y2).(-3x3)
e)(x2 -2x+3). (x-4) f) ( 2x3 -3x -1). (5x+2)
g) ( 25x2 + 10xy + 4y2). ( ( 5x – 2y) h) ( 5x3 – x2 + 2x – 3). ( 4x2 – x + 2)
a) \(2x\left(x^2-7x-3\right)=2x.x^2-2x.7x-2x.3=2x^3-14x^2-6x\)
b) \(\left(-2x^3+y^2-7xy\right)4xy^2=\left(-2x^3\right)4xy^2+y^24xy^2-7xy.4xy^2=-8x^4y^2+4xy^4-28x^2y^3\)
c) \(\left(-5x^3\right)\left(2x^2+3x-5\right)=-5x^32x^2-5x^33x-5x^3.-5=-10x^5-15x^4+25x^3\)
d) \(\left(2x^2-xy+y^2\right)\left(-3x^3\right)=-3x^32x^2-3x^3.-xy-3x^3y^2=-6x^5+3x^4y-3x^3y^2\)
e) \(\left(x^2-2x+3\right)\left(x-4\right)=x\left(x^2-2x+3\right)-4\left(x^2-2x+3\right)=x^3-2x^2+3x-4x^2+8x-12=x^3-6x^2+11x-12\)
f) \(\left(2x^3-3x-1\right)\left(5x+2\right)=5x\left(2x^3-3x-1\right)+2\left(2x^3-3x-1\right)=10x^4-15x^2-5x+4x^3-6x-2=10x^4+4x^3-15x^2-11x-2\)
g)
\(\left(25x^2+10xy+4y^2\right).\left((5x-2y\right)\)
\(=125x^3-50x^2y+20x^2y-20xy^2+20xy^2-8y^3\)
\(=125x^3-30x^2y+8y^3\)
h)
\(\left(5x^3-x^2+2x-3\right)\left(4x^2-x+2\right)\)
\(=20x^5-5x^4+10x^3-4x^4+x^3-2x^2+8x^3-2x^2+4x-12x^2+3x-6\)
\(=20x^5-9x^4+19x^3-16x^2+7x-6\)
giải phương trình sau:
a. (9x2-4)(x+1) = (3x+2) (x2-1)
b. (x-1)2-1+x2 = (1-x)(x+3)
c. (x2-1)(x+2)(x-3) = (x-1)(x2-4)(x+5)
d. x4+x3+x+1=0
e. x3-7x+6 = 0
f. x4-4x3+12x-9 = 0
g. x5-5x3+4x = 0
h. x4-4x3+3x2+4x-4 = 0
m.n jup vs
1,phân tích mỗi đa thức sau thành phân tử
a,(x+2y)2-(x-y)2
b,(x+1)3+(x-1)3
c,9x2-3x+2y-4y2
d,4x2-4xy+2x-y+y2
e,x3+3x2+3x+1-y3
g,x3-2x2y+xy2-4x
a) \(\left(x+2y\right)^2-\left(x-y\right)^2=\left(x+2y+x-y\right)\left(x+2y-x+y\right)\)
\(=\left(2x+y\right).3y\)
b) \(\left(x+1\right)^3+\left(x-1\right)^3\)
\(=\left(x+1+x-1\right)\left[\left(x+1\right)^2-\left(x+1\right)\left(x-1\right)+\left(x-1\right)^2\right]\)
\(=2x\left[\left(x+1\right)^2-\left(x^2-1\right)+\left(x-1\right)^2\right]\)
c) \(9x^2-3x+2y-4y^2\)
\(=9x^2-4y^2-3x+2y\)
\(=\left(3x-2y\right)\left(3x+2y\right)-\left(3x-2y\right)\)
\(=\left(3x-2y\right)\left[3x+2y-1\right]\)
d) \(4x^2-4xy+2x-y+y^2\)
\(=4x^2-4xy+y^2+2x-y\)
\(=\left(2x-y\right)^2+2x-y\)
\(=\left(2x-y\right)\left(2x-y+1\right)\)
e) \(x^3+3x^2+3x+1-y^3\)
\(=\left(x+1\right)^3-y^3\)
\(=\left(x+1-y\right)\left[\left(x+1\right)^2+y\left(x+1\right)+y^2\right]\)
g) \(x^3-2x^2y+xy^2-4x\)
\(=x\left(x^2-2xy+y^2\right)-4x\)
\(=x\left(x-y\right)^2-4x\)
\(=x\left[\left(x-y\right)^2-4\right]\)
\(=x\left(x-y+2\right)\left(x-y-2\right)\)
a) (x + 2y)² - (x - y)²
= (x + 2y - x + y)(x + 2y + x - y)
= 3y(2x + y)
b) (x + 1)³ + (x - 1)³
= (x + 1 + x - 1)[(x + 1)² - (x + 1)(x - 1) + (x - 1)²]
= 2x(x² + 2x + 1 - x² + 1 + x² - 2x + 1)
= 2x(x² + 3)
c) 9x² - 3x + 2y - 4y²
= (9x² - 4y²) - (3x - 2y)
= (3x - 2y)(3x + 2y) - (3x - 2y)
= (3x - 2y)(3x + 2y - 1)
d) 4x² - 4xy + 2x - y + y²
= (4x² - 4xy + y²) + (2x - y)
= (2x - y)² + (2x - y)
= (2x - y)(2x - y + 1)
e) x³ + 3x² + 3x + 1 - y³
= (x³ + 3x² + 3x + 1) - y³
= (x + 1)³ - y³
= (x + 1 - y)[(x + 1)² + (x + 1)y + y²]
= (x - y + 1)(x² + 2x + 1 + xy + y + y²)
g) x³ - 2x²y + xy² - 4x
= x(x² - 2xy + y² - 4)
= x[(x² - 2xy + y²) - 4]
= x[(x - y)² - 2²]
= x(x - y - 2)(x - y + 2)
Phân tích các đa thức sau thành nhân tử:
a/ 2x3 + 3x2 + 2x +3 b/ x2 – x – 12 c/ 4x2 –( x2 + 1)2
d/ 4xy2 – 12x2y + 8xy e/ x2 + x – 6 f/ x3 + 2x2y + xy2 – 4xz2
g/ x3 – 2x2y + xy2 – 25x h/ x2 – 2x – 3 i/ x3 – 3x2 – 9x + 27
a: \(=x^2\left(2x+3\right)+\left(2x+3\right)\)
\(=\left(2x+3\right)\left(x^2+1\right)\)
b: \(=\left(x-4\right)\left(x+3\right)\)
e: =(x+3)(x-2)
a) \(=x^2\left(2x+3\right)+\left(2x+3\right)=\left(2x+3\right)\left(x^2+1\right)\)
b) \(=x\left(x-4\right)+3\left(x-4\right)=\left(x-4\right)\left(x+3\right)\)
c) \(=\left(2x\right)^2-\left(x^2+1\right)^2=\left(x^2-2x+1\right)\left(x^2+2x+1\right)=\left(x-1\right)^2\left(x+1\right)^2\)
d) \(=4xy\left(y-3x+2\right)\)
e) \(=x\left(x-2\right)+3\left(x-2\right)=\left(x-2\right)\left(x+3\right)\)
f) \(=x\left(x^2+2xy+y^2-4z^2\right)=x\left[\left(x+y\right)^2-4z^2\right]=x\left(x+y-2z\right)\left(x+y+2z\right)\)
g) \(=x\left(x^2-2xy+y^2-25\right)=x\left[\left(x-y\right)^2-25\right]=x\left(x-y-5\right)\left(x-y+5\right)\)
h) \(=x\left(x+1\right)-3\left(x+1\right)=\left(x+1\right)\left(x-3\right)\)
i) \(=x^2\left(x-3\right)-9\left(x-3\right)=\left(x-3\right)\left(x^2-9\right)=\left(x-3\right)^2\left(x+3\right)\)
a) 2x. (x2 – 7x -3)
b) ( -2x3 + y2 -7xy). 4xy2
c)(-5x3). (2x2+3x-5)
d) (2x2 - xy+ y2).(-3x3)
e)(x2 -2x+3). (x-4)
f) ( 2x3 -3x -1). (5x+2)
g) ( 25x2 + 10xy + 4y2). ( 5x – 2y)
h) ( 5x3 – x2 + 2x – 3). ( 4x2 – x + 2)
a,\(4x^2-14x^2-6x=-10x^2-6x\)
các câu còn lại làm tg tuj
a) 2x.(x2 - 7x - 3)
= 2xx2 + 2x(-7x) + 2x(-3)
= 2x2x - 2.7xx - 2.3x
= 2x3 - 14x2 - 6x
Bài 2: Phân tích các đa thức sau thành nhân tử
a) x2 – 9 b) 4x2 -1 c) x4 - 16
d) x2 – 4x + 4 e) x3 – 8 f) x3 + 3x2 + 3x + 1
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