Thu gọn các đa thức ( làm nhanh giúp mình với )
A= 4x2 -3x+7x2+2x-5
B= 3x +7y – 6x – 8 +y – 2
C=4xy -2x2y-xy+3x2y+7
D= 6x4 -3x2 +x2 -4x + 3x4 –x +2
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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)
`@` `\text {Ans}`
`\downarrow`
`1.`
\(\left(-4xy\right)\cdot\left(2xy^2-3x^2y\right)\)
`=`\(\left(-4xy\right)\left(2xy^2\right)+\left(-4xy\right)\left(-3x^2y\right)\)
`=`\(-8\left(x\cdot x\right)\left(y\cdot y^2\right)+12\left(x\cdot x^2\right)\left(y\cdot y\right)\)
`=`\(-8x^2y^3+12x^3y^2\)
`2.`
\(\left(-5x\right)\left(3x^3+7x^2-x\right)\)
`=`\(\left(-5x\right)\left(3x^3\right)+\left(-5x\right)\left(7x^2\right)+\left(-5x\right)\left(-x\right)\)
`=`\(-15x^4-35x^3+5x^2\)
`3.`
\(\left(3x-2\right)\left(4x+5\right)-6x\left(2x-1\right)\)
`=`\(3x\left(4x+5\right)-2\left(4x+5\right)-12x^2+6x\)
`=`\(12x^2+15x-8x-10-12x^2+6x\)
`=`\(\left(12x^2-12x^2\right)+\left(15x-8x+6x\right)-10\)
`=`\(13x-10\)
`4.`
\(2x^2\left(x^2-7x+9\right)\)
`=`\(2x^2\cdot x^2+2x^2\cdot\left(-7x\right)+2x^2\cdot9\)
`=`\(2x^4-14x^3+18x^2\)
`5.`
\(\left(3x-5\right)\left(x^2-5x+7\right)\)
`=`\(3x\left(x^2-5x+7\right)-5\left(x^2-5x+7\right)\)
`=`\(3x^3-15x^2+21x-5x^2+25x-35\)
`=`\(3x^3-20x^2+46x-35\)
a) Đặt A(x)=0
\(\Leftrightarrow-4x-5=0\)
\(\Leftrightarrow-4x=5\)
hay \(x=-\dfrac{5}{4}\)
b) Đặt B(x)=0
\(\Leftrightarrow3\left(2x-1\right)-2\left(x+1\right)=0\)
\(\Leftrightarrow6x-3-2x-2=0\)
\(\Leftrightarrow4x=5\)
hay \(x=\dfrac{5}{4}\)
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:
\(a,=20x^3-10x^2+5x-20x^3+10x^2+4x=9x\\ b,=3x^2-6x-5x+5x^2-8x^2+24=24-11x\\ c,=x^5+x^3-2x^3-2x=x^5-x^3-2x\)
a) \(...=P\left(x\right)=2x^4-x^4+3x^3+4x^2-3x^2+3x-x+3\)
\(P\left(x\right)=x^4+3x^3+x^2+2x+3\)
\(...=Q\left(x\right)=x^4+x^3+3x^2-x^2+4x+4-2\)
\(Q\left(x\right)=x^4+x^3+2x^2+4x+2\)
b) \(P\left(x\right)+Q\left(x\right)=\left(x^4+3x^3+x^2+2x+3\right)+\left(x^4+x^3+2x^2+4x+2\right)\)
\(\Rightarrow P\left(x\right)+Q\left(x\right)=2x^4+4x^3+3x^2+6x+5\)
\(P\left(x\right)-Q\left(x\right)=\left(x^4+3x^3+x^2+2x+3\right)-\left(x^4+x^3+2x^2+4x+2\right)\)
\(\)\(\Rightarrow P\left(x\right)-Q\left(x\right)=x^4+3x^3+x^2+2x+3-x^4-x^3-2x^2-4x-2\)
\(\Rightarrow P\left(x\right)-Q\left(x\right)=2x^3-x^2-2x+1\)
1b.=2((x+y)+(x+y)(x-y)+(x-y))=2(x2-y2+x+y+x-y)=2(x2-y2+2x)=2x2-2y2+4x
2a.=4xy+4xy+2y=8xy+2y=2y(4x+1)
b.=(3x)2+2.3x.y+y2-(2z)2=(3x+y)2-(2z)2=(3x+y-2z)(3x+y+2z)
c.=x2-x-7x+7=x(x-1)-7(x-1)=(x-1)(x-7)
\(\left(x+y\right)^2+2\left(x+y\right)\left(x-y\right)+\left(x-y\right)^2\)
\(=\left(x+y+x-y\right)^2\)
\(=\left(2x\right)^2\)
\(=4x^2\)
hk tốt
^^
a, \(A=2x^2+x+6\)
Với x = 1 suy ra A = 2 + 1 + 6 = 9
Với x = 1/2 suy ra A = 1/2 + 1/2 + 6 = 7
b, \(B=7x-6y-5\)Thay x = 3 ; y = -2 ta được
B = 7.3 - 6 ( - 2 ) - 5 = 21 + 12 - 5 = 33 - 5 = 28
\(a,=4x^2+3xy-y^2+4xy-4x^2=7xy-y^2\\ b,=x^2-9-x^3+3x+x^2-3=-x^3+2x^2+3x-12\\ c,=-2x^2+12x-18+5x^2+4x-1=3x^2+16x-19\\ d,=8x^3+1-3x^3+6x^2=5x^3+6x^2+1\\ e,=\left(3x^2+4x+15x+20\right):\left(3x+4\right)\\ =\left(3x+4\right)\left(x+5\right):\left(3x+4\right)\\ =x+5\\ f,=\left(x^3+4x^2-3x+3x^2+12x-9+3x+3\right):\left(x^2+4x-3\right)\\ =\left[\left(x^2+4x-3\right)\left(x+3\right)+3x+3\right]:\left(x^2+4x-3\right)\\ =x+3\left(dư.3x+3\right)\)
Bài 1
a) (15x4 - 8x3 + 3x2) : 3x2 = 15x4 : 3x2 - 8x3 : 3x2 + 3x2 : 3x2 = 5x2 - \(\dfrac{8}{3}x\) + 1
b) (4x2 - 4xy + y2) : (2x - y) = (2x - y)2 : (2x - y) = 2x - y
c) dùng phương pháp chia đa thức 1 biến đã sắp xếp nha
d) (x2 - 2x + 1) : (x - 1) = (x - 1)2 : (x - 1) = x - 1
Bài 2
a) x2 + 3x + 3xy + 9xy = x2 + 3x + 12xy = x (x + 3 + 4y)
b) x2 - y2 + 2x + 1 = x2 + 2x + 1 - y2 = (x + 1)2 - y2 = (x + 1 - y)(x + 1 + y)
c) x2 - xy + x - y = x (x - y) + (x - y) = (x - y)(x + 1)
x4,x2,y2 là mũ nhá các bn
giúp mk nhanh lên mình sắp phải nộp r
A = \(4x^2-3x+7x^2+2x-5\)
\(11x^2-3x+2x-5\)
\(11x^2-x-5\)
B = \(3x+7y-6x-8+y-2\)
\(3x+7y-6x-10+y\)
\(- 3x+7y-10+y\)
\(3x+8y-10\)
C = chịu
D= \(6x^4-3x^2+x^2-4x+3.4-x+2\)
\(6x^4-3x^2+x^2-4x;12-x+2\\ \)
\(6x^4-3x^2+x^2-4x+14-x\)
\(6x^4-2x^2-4x+14-x\)
\(6x^4-2x^2-5x+14\)