Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
a: \(A=-5x^3+9x^3-2x^2-2x^2+x-x+1\)
\(=4x^3-4x^2+1\)
\(B=-4x^3+2x^3-2x^2+2x^2+6x-9x-2\)
\(=-2x^3-3x-2\)
\(C=x^3-6x^2+2x-4\)
b: \(A\left(x\right)+B\left(x\right)-C\left(x\right)\)
\(=4x^3-4x^2+1-2x^3-3x-2+x^3-6x^2+2x-4\)
\(=3x^3-10x^2-x-4\)
\(A=\left[6y^3-3y^2+y+1\right]-y-y^2-y^3-y^2\)
\(=5y^3-5y^2+1\)
\(B=2ax^2-2x^2-a-a+x^2+ax=2ax^2-x^2-2a+ax\)
\(C=\left(p^3+1+2p^3+6p^2-2p^3\right)\cdot3p^2-3p^5\)
\(=\left(p^3+6p^2+1\right).3p^2-3p^5=18p^4+3p^2\)
a) Ta có: \(B\left(x\right)=-2x^3+2x^2+12+5x^2-9x\)
\(=-2x^3+7x^2-9x+12\)
b) Ta có: A(x)+B(x)
\(=4x^3-7x^2+3x-12-2x^3+7x^2-9x+12\)
\(=2x^3-6x\)
b) Ta có: A(x)-B(x)
\(=4x^3-7x^2+3x-12+2x^3-7x^2+9x-12\)
\(=6x^3-14x^2+12x-24\)
2,
M + N = 3xyz - 3x2 + 5xy - 1 + 5x2 + xyz - 5xy + 3 - y
= -3x2 + 5x2 + 3xyz + xyz + 5xy - 5xy - y - 1 + 3
= 2x2 + 4xyz - y +2.
M - N = (3xyz - 3x2 + 5xy - 1) - (5x2 + xyz - 5xy + 3 - y)
= 3xyz - 3x2 + 5xy - 1 - 5x2 - xyz + 5xy - 3 + y
= -3x2 - 5x2 + 3xyz - xyz + 5xy + 5xy + y - 1 - 3
= -8x2 + 2xyz + 10xy + y - 4.
N - M = (5x2 + xyz - 5xy + 3 - y) - (3xyz - 3x2 + 5xy - 1)
= 5x2 + xyz - 5xy + 3 - y - 3xyz + 3x2 - 5xy + 1
= 5x2 + 3x2 + xyz - 3xyz - 5xy - 5xy - y + 3 + 1
= 8x2 - 2xyz - 10xy - y + 4.
3,
a) P + (x2 – 2y2) = x2 – y2 + 3y2 – 1
P = (x2 – y2 + 3y2 – 1) - (x2 – 2y2)
P = x2 – y2 + 3y2 – 1 - x2 + 2y2
P = x2 – x2 – y2 + 3y2 + 2y2 – 1
P = 4y2 – 1.
Vậy P = 4y2 – 1.
b) Q – (5x2 – xyz) = xy + 2x2 – 3xyz + 5
Q = (xy + 2x2 – 3xyz + 5) + (5x2 – xyz)
Q = xy + 2x2 – 3xyz + 5 + 5x2 – xyz
Q = 7x2 – 4xyz + xy + 5
Vậy Q = 7x2 – 4xyz + xy + 5.
4,
a, Thu gọn : x2+2xy-3x3+2y3+3x3-y3
= x2+2xy+(-3x3+3x3)+2y3-y3
=x2+2xy+2y3-y3
Thay x=5,y=4 vào đa thức x2+2xy+2y3-y3 Ta có:
52 + 2.5.4 + 43 = 25 + 40 + 64 = 129.
Vậy giá trị của đa thức x2+2xy+2y3-y3 tại x=5,y=4 là 129
b,
Thay x = -1; y = -1 vào biểu thức xy-x2y2+x4y4-x6y6+x8y8 Ta Có
M = (-1)(-1) - (-1)2.(-1)2 + (-1)4. (-1)4-(-1)6.(-1)6 + (-1)8.(-1)8
= 1 -1 + 1 - 1+ 1 = 1.
Vậy giá trị của biểu thức xy-x2y2+x4y4-x6y6+x8y8 tại x=-1, y=-1 là 1
5,
a, C=A+B
C = x2 – 2y + xy + 1 + x2 + y - x2y2 - 1
C = 2x2 – y + xy - x2y2
b) C + A = B => C = B - A
C = (x2 + y - x2y2 - 1) - (x2 – 2y + xy + 1)
C = x2 + y - x2y2 - 1 - x2 + 2y - xy - 1
C = - x2y2 - xy + 3y - 2.
1) a)
\(A\left(x\right)=x^3+5x-7x^2-2x-12+3x^3\\ \text{ }=\left(x^3+3x^3\right)-7x^2+\left(5x-2x\right)-12\\ \text{ }=4x^3-7x^2+3x-12\)
\(B\left(x\right)=-2x^3+2x^2+12+5x^2-9x\\ \text{ }=-2x^3+\left(2x^2+5x^2\right)-9x+12\\ \text{ }=-2x^3+7x^2-9x+12\)
b)
\(A\left(x\right)+B\left(x\right)=\left(4x^3-7x^2+3x-12\right)+\left(-2x^3+7x^2-9x+12\right)\\ \text{ }=4x^3-7x^2+3x-12-2x^3+7x^2-9x+12\\ \text{ }=\left(4x^3-2x^3\right)+\left(7x^2-7x^2\right)-\left(9x-3x\right)+\left(12-12\right)\\ \text{ }=2x^3-6x\)
\(B\left(x\right)-A\left(x\right)=\left(-2x^3+7x^2-9x+12\right)-\left(4x^3-7x^2+3x-12\right)\\ \text{ }=-2x^3+7x^2-9x+12-4x^3+7x^2-3x+12\\ \text{ }=\left(-2x^3-4x^3\right)+\left(7x^2+7x^2\right)-\left(9x+3x\right)+\left(12+12\right)\\ \text{ }=6x^3+14x^2-12x+24\)
\(\left(4x-7\right)\cdot\left(x+5\right)\\ =4x\left(x+5\right)-7\left(x+5\right)\\ =4x\cdot x+4x\cdot5-7\cdot x-7\cdot5\\ =4x^2+20x-7x-35\)
\(a,N\left(x\right)=x^2+3x^4-2x-x^2+2x^3=3x^4+2x^3+\left(x^2-x^2\right)-2x\\ =3x^4+2x^3-2x\\ P\left(x\right)=-8+5x-6x^3-4x+6=-6x^3+\left(5x-4x\right)+\left(-8+6\right)\\ =-6x^3+x-2\)
Bậc của N(x) là 4
Bậc của P(x) là 3
\(b,P\left(x\right)+N\left(x\right)=3x^4+2x^3-2x-6x^3+x-2\\ =3x^4+\left(2x^3-6x^3\right)+\left(-2x+x\right)-2\\ =3x^4-4x^3-x-2\)
\(c,B\left(x\right)=-2x^2\left(x^3-2x+5x^2-1\right)\\ =\left(-2x^2\right).x^3+\left(-2x^2\right).\left(-2x\right)+\left(-2x^2\right).5x^2+\left(-2x^2\right).\left(-1\right)\\ =-2x^5+4x^3-10x^4+2x^2\\ =-2x^5-10x^4+4x^3+2x^2\)
Thu gọn đa thức
a,A=2x2 +x-\(\dfrac{1}{2}\)x2+5x+3
b,B=5xy+\(\dfrac{1}{2}\)x2y-\(\dfrac{2}{3}\)xy+2x2y
a: \(A=\dfrac{3}{2}x^2+6x+3\)
b: \(B=5xy-\dfrac{2}{3}xy+\dfrac{1}{2}x^2y+2x^2y=\dfrac{5}{2}x^2y+\dfrac{13}{3}xy\)
a) \(2x^2+x-\dfrac{1}{2}x^2+5x+3\)\(\)
= \(\left(2x-\dfrac{1}{2}x^2\right)+\left(x+5x\right)+3\)
= \(\dfrac{3}{2}x^2+6x+3\)
Vậy A = \(\dfrac{3}{2}x^2+6x+3\)
a) \(\left\{{}\begin{matrix}M=x^2y-2xy+6-xy=x^2y-3xy+6\\N=-2x^2y+2xy+x^2y-3=-x^2y+2xy-3\end{matrix}\right.\)
b) \(x=1;y=2\Rightarrow M=1^2.2-2.1.2+6-1.2=2\)
c) \(M+N\Rightarrow x^2y-3xy+6+\left(-x^2y\right)+2xy-3=-xy+3\)
