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\(\begin{array}{l}A + B + C\\ = (3{x^4} - 2{x^3} - x + 1) + ( - 2{x^3} + 4{x^2} + 5x) + ( - 3{x^4} + 2{x^2} + 5)\\ = 3{x^4} - 2{x^3} - x + 1 - 2{x^3} + 4{x^2} + 5x - 3{x^4} + 2{x^2} + 5\\ = (3{x^4} - 3{x^4}) + ( - 2{x^3} - 2{x^3}) + (4{x^2} + 2{x^2}) + ( - x + 5x) + (1 + 5)\\ = 0 + ( - 4{x^3}) + 6{x^2} + 4x + 6\\ = - 4{x^3} + 6{x^2} + 4x + 6\\A - B + C\\ = (3{x^4} - 2{x^3} - x + 1) - ( - 2{x^3} + 4{x^2} + 5x) + ( - 3{x^4} + 2{x^2} + 5)\\ = 3{x^4} - 2{x^3} - x + 1 + 2{x^3} - 4{x^2} - 5x - 3{x^4} + 2{x^2} + 5\\ = (3{x^4} - 3{x^4}) + ( - 2{x^3} + 2{x^3}) + ( - 4{x^2} + 2{x^2}) + ( - x - 5x) + (1 + 5)\\ = 0 + 0 + ( - 2{x^2}) - 6x + 6\\ = - 2{x^2} - 6x + 6\\A - B - C\\ = (3{x^4} - 2{x^3} - x + 1) - ( - 2{x^3} + 4{x^2} + 5x) - ( - 3{x^4} + 2{x^2} + 5)\\ = 3{x^4} - 2{x^3} - x + 1 + 2{x^3} - 4{x^2} - 5x + 3{x^4} - 2{x^2} - 5\\ = (3{x^4} + 3{x^4}) + ( - 2{x^3} + 2{x^3}) + ( - 4{x^2} - 2{x^2}) + ( - x - 5x) + (1 - 5)\\ = 6{x^4} + 0 + ( - 6{x^2}) - 6x + ( - 4)\\ = 6{x^4} - 6{x^2} - 6x - 4\end{array}\)
`@` `\text {Ans}`
`\downarrow`
`B(x)-A(x)+C(x)`
`=`\((x^2-5x^3-4x+7) - (-x^3 + 7x^2 +2x - 15) + 3x^3 - 7x^2 -4\)
`=`\(x^2-5x^3-4x+7+x^3-7x^2-2x+15+3x^3-7x^2-4\)
`=`\(\left(-5x^3+x^3+3x^3\right)+\left(x^2-7x^2-7x^2\right)+\left(-4x-2x\right)+\left(7+15-4\right)\)
`=`\(-x^3-13x^2-6x+18\)
`C(x)-B(x)-A(x)`
`=`\(3x^3 - 7x^2 -4 - (x^2-5x^3-4x+7) - (-x^3 + 7x^2 +2x - 15)\)
`=`\(3x^3-7x^2-4-x^2+5x^3+4x-7+x^3-7x^2-2x+15\)
`=`\(\left(3x^3+5x^3+x^3\right)+\left(-7x^2-x^2-7x^2\right)+\left(4x-2x\right)+\left(-4-7+15\right)\)
`=`\(9x^3-15x^2+2x+4\)
a) \(B\left(x\right)-A\left(x\right)+C\left(x\right)\)
\(=\left(x^2-5x^3-4x+7\right)-\left(-x^3+7x^2+2x-15\right)+\left(3x^3-7x^2-4\right)\)
\(=x^2-5x^3-4x+7+x^3-7x^2-2x+15+3x^3-7x^2-4\)
\(=\left(-5x^3+x^3+3x^3\right)+\left(x^2-7x^2-7x^2\right)-\left(4x+2x\right)+\left(7-4+15\right)\)
\(=-x^3-13x^2-6x+18\)
b) \(C\left(x\right)-B\left(x\right)-A\left(x\right)\)
\(=\left(3x^3-7x^2-4\right)-\left(x^2-5x^3-4x+7\right)-\left(-x^3+7x^2+2x-15\right)\)
\(=3x^3-7x^2-4-x^2+5x^3+4x-7+x^3-7x^2-2x+15\)
\(=\left(3x^3+5x^3+x^3\right)-\left(7x^2+x^2+7x^2\right)+\left(4x-2x\right)-\left(4+7-15\right)\)
\(=9x^3-15x^2+2x+4\)
\(\begin{array}{l}A + B = (6{x^4} - 4{x^3} + x - \dfrac{1}{3}) + ( - 3{x^4} - 2{x^3} - 5{x^2} + x + \dfrac{2}{3})\\ = 6{x^4} - 4{x^3} + x - \dfrac{1}{3} - 3{x^4} - 2{x^3} - 5{x^2} + x + \dfrac{2}{3}\\ = (6{x^4} - 3{x^4}) + ( - 4{x^3} - 2{x^3}) - 5{x^2} + (x + x) + ( - \dfrac{1}{3} + \dfrac{2}{3})\\ = 3{x^4} - 6{x^3} - 5{x^2} + 2x + \dfrac{1}{3}\\A - B = (6{x^4} - 4{x^3} + x - \dfrac{1}{3}) - ( - 3{x^4} - 2{x^3} - 5{x^2} + x + \dfrac{2}{3})\\ = 6{x^4} - 4{x^3} + x - \dfrac{1}{3} + 3{x^4} + 2{x^3} + 5{x^2} - x - \dfrac{2}{3}\\ = (6{x^4} + 3{x^4}) + ( - 4{x^3} + 2{x^3}) + 5{x^2} + (x - x) + ( - \dfrac{1}{3} - \dfrac{2}{3})\\ = 9{x^4} - 2{x^3} + 5{x^2} - 1\end{array}\)\(\begin{array}{l}A + B = (6{x^4} - 4{x^3} + x - \dfrac{1}{3}) + ( - 3{x^4} - 2{x^3} - 5{x^2} + x + \dfrac{2}{3})\\ = 6{x^4} - 4{x^3} + x - \dfrac{1}{3} - 3{x^4} - 2{x^3} - 5{x^2} + x + \dfrac{2}{3}\\ = (6{x^4} - 3{x^4}) + ( - 4{x^3} - 2{x^3}) - 5{x^2} + (x + x) + ( - \dfrac{1}{3} + \dfrac{2}{3})\\ = 3{x^4} - 6{x^3} - 5{x^2} + 2x + \dfrac{1}{3}\\A - B = (6{x^4} - 4{x^3} + x - \dfrac{1}{3}) - ( - 3{x^4} - 2{x^3} - 5{x^2} + x + \dfrac{2}{3})\\ = 6{x^4} - 4{x^3} + x - \dfrac{1}{3} + 3{x^4} + 2{x^3} + 5{x^2} - x - \dfrac{2}{3}\\ = (6{x^4} + 3{x^4}) + ( - 4{x^3} + 2{x^3}) + 5{x^2} + (x - x) + ( - \dfrac{1}{3} - \dfrac{2}{3})\\ = 9{x^4} - 2{x^3} + 5{x^2} - 1\end{array}\)
1 ) a) \(4x^2-x^2+8x^2\)
\(=\left(4+8\right).x^2+x^2-x^2\)
\(=12.x^3\)
b) \(\frac{1}{2}.x^2.y^2-\frac{3}{4}.x^2.y^2+x^2.y^2\)
\(\left(\frac{1}{2}-\frac{3}{4}\right).x^2.x^2.x^2.+y^2+y^2+y^2\)
\(=-\frac{1}{4}.x^6+y^6\)
c) \(3y-7y+4y-6y\)
\(=\left(3-7+4-6\right).y.y.y.y\)
\(=-6.y^4\)
2)
\(\left(-\frac{2}{3}.y^3\right)+3y^2-\frac{1}{2}.y^3-y^2\)
\(\left(-\frac{2}{3}+3-\frac{1}{2}\right).y^3.y^3-y\)
\(=\frac{25}{6}.y^5\)
b) \(5x^3-3x^2+x-x^3-4x^2-x\)
\(=\left(5-3-4\right).\left(x^3.x^2+x-x^3-x^2-x\right)\)
\(=-2.0=0\)
hông chắc
3)a) \(5xy^2.\frac{1}{2}x^2y^2x\)
\(\left(5.\frac{1}{2}\right).x^2.x^2.x.y^2.y^2\)
\(=\frac{5}{2}.x^5.y^4\)
b) Tổng các bậc của đơn thức là
5+4 = 9
Hệ số của đơn thức là \(\frac{5}{2}\)
Phần biến là x;y
Thay x=1;y=-1 vào đơn thức
\(\frac{5}{2}.1^5.\left(-1\right)^4\)
\(\frac{5}{2}.1.\left(-1\right)\)
\(\frac{5}{2}.\left(-1\right)=-\frac{5}{2}\)
Vậy ....
chắc không đúng đâu uwu
a, Ta có \(\left(a-3+15\right)x^2y^3=4x^2y^3\Rightarrow a+12=4\Leftrightarrow a=-8\)
b, \(10ax^6y^6=-20x^6y^6\Rightarrow10a=-20\Leftrightarrow a=-2\)
\(\left(\dfrac{3}{2}\right)^5\cdot x=\left(\dfrac{3}{2}\right)^7\)
=>\(x=\left(\dfrac{3}{2}\right)^7:\left(\dfrac{3}{2}\right)^5=\left(\dfrac{3}{2}\right)^2=\dfrac{9}{4}\)