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ST
12 tháng 9 2015
6853 + 3153 = ( 685 + 315 ) . ( 8652 + 685 . 315 + 3152 ) = 1 000.
Vì các số hạng trong ngoặc đều chia hết cho 25 nên 8653 + 3153 chia hết cho 25 000.
MH
14 tháng 9 2021
a) ^A+^A1=180 độ( kề bù)
^C+^C1=180 độ (kề bù)
⇒^A+^A1+^C+^C1=180+180=360 độ
11 tháng 6 2023
a: \(=\dfrac{2x^3+x^2-6x^2-3x+2x+1}{2x+1}=2x^2-3x+1\)
b: \(=\dfrac{x^3+2x^2-2x^2-4x+2x+4}{x+2}=x^2-2x+2\)
d: \(=\dfrac{\left(x^2-1\right)\left(x^2+1\right)-2x\left(x^2-1\right)}{x^2-1}=\left(x-1\right)^2\)
h: \(=\dfrac{x^3+x^2-3x^2-3x+8x+8}{x+1}=x^2-3x+8\)
11 tháng 6 2023
\(c,\)
\(\left(6x^3-19x^2+23x-12\right):\left(2x-3\right)\)
\(=\left(6x^3-10x^2-9x^2+8x+15x-12\right):\left(2x-3\right)\)
\(=\left[\left(6x^3-10x^2+8x\right)-\left(9x^2-15x+12\right)\right]:\left(2x-3\right)\)
\(=\left[2x\left(3x^2-5x+4\right)-3\left(3x^2-5x+4\right)\right]:\left(2x-3\right)\)
\(=\left[\left(3x^2-5x+4\right)\left(2x-3\right)\right]:\left(2x-3\right)\)
\(=3x^2-5x+4\)
\(e,\)
\(\left(6x^3-5x^2+4x-1\right):\left(2x^2-x+1\right)\)
\(=\left(6x^3-3x^2-2x^2+3x+x-1\right):\left(2x^2-x+1\right)\)
\(=\left[\left(6x^3-3x^2+3x\right)-\left(2x^2-x+1\right)\right]:\left(2x^2-x+1\right)\)
\(=\left[3x\left(2x^2-x+1\right)-\left(2x^2-x+1\right)\right]:\left(2x^2-x+1\right)\)
\(=\left[\left(2x^2-x+1\right)\left(3x-1\right)\right]:\left(2x^2-x+1\right)\)
\(=3x-1\)
\(f,\)
\(\left(x^3-2x^2-5x+6\right):\left(x+2\right)\)
\(=\left(x^3-4x^2+2x^2+3x-8x+6\right):\left(x+2\right)\)
\(=\left[\left(x^3+2x^2\right)-\left(4x^2+8x\right)+\left(3x+6\right)\right]\)
\(=\left[x^2\left(x+2\right)-4x\left(x+2\right)+3\left(x+2\right)\right]\)
\(=\left[\left(x+2\right)\left(x^2-4x+3\right)\right]:\left(x+2\right)\)
\(=x^2-4x+3\)
\(g,\)
\(\left(x^3-2x^2-5x+6\right):\left(x+2\right)\)
\(=\left(x^3+2x^2-4x^2-8x+3x+6\right):\left(x+2\right)\)
\(=\left[\left(x^3+2x^2\right)-\left(4x^2+8x\right)+\left(3x+6\right)\right]:\left(x+2\right)\)
\(=\left[x^2\left(x+2\right)-4x\left(x+2\right)+3\left(x+2\right)\right]:\left(x+2\right)\)
\(=\left[\left(x+2\right)\left(x^2-4x+3\right)\right]:\left(x+2\right)\)
\(=x^2-4x+3\)
17 tháng 12 2023
a: \(M=2\left(x+5\right)^2+5\left(x-2\right)^2-7\left(x+3\right)\left(x-3\right)\)
\(=2\left(x^2+10x+25\right)+5\left(x^2-4x+4\right)-7\left(x^2-9\right)\)
\(=2x^2+20x+50+5x^2-20x+20-7x^2+63\)
\(=113\)
b: \(H=\left(2x-3y\right)^2-\left(3y-2\right)\left(3y+2\right)-\left(1-2x\right)^2+4x\left(3y-1\right)\)
\(=4x^2-12xy+9y^2+12xy-4x-\left(9y^2-4\right)-\left(4x^2-4x+1\right)\)
\(=4x^2+9y^2-4x-9y^2+4-4x^2+4x-1\)
=3
c: \(N=\left(2x+3y\right)^2+\left(3x-2y\right)^2-13\left(x+y\right)\left(x-y\right)-26\left(y+1\right)\left(y-1\right)\)
\(=4x^2+12xy+9y^2+9x^2-12xy+4y^2-13\left(x^2-y^2\right)-26\left(y^2-1\right)\)
\(=13x^2+13y^2-13x^2+13y^2-26y^2+26\)
=26
d: \(K=\left(x^2y-3\right)^2-\left(2x-y\right)^3+xy^2\left(6-x^3\right)+8x^3-6x^2y-y^3\)
\(=x^4y^2-6x^2y+9+6xy^2-x^4y^2+8x^3-6x^2y-y^3-\left(2x-y\right)^3\)
\(=-12x^2y+9-y^3+6xy^2+8x^3-\left(8x^3-12x^2y+6xy^2-y^3\right)\)
\(=\left(8x^3-12x^2y+6xy^2-y^3\right)-\left(8x^3-12x^2y+6xy^2-y^3\right)+9\)
=9
e: \(P=\left(4x+3\right)\left(16x^2-12x+9\right)-\left(-23+64x^3\right)\)
\(=\left(4x\right)^3+3^3+23-64x^3\)
\(=64x^3+27+23-64x^3\)
=50
h: \(Q=\left(x+5y\right)\left(x^2-5xy+25y^2\right)+\left(x-5y\right)\left(x^2+5xy+25y^2\right)-\dfrac{1}{2}\left(4x^3-7\right)\)
\(=x^3+125y^3+x^3-125y^3-2x^3+\dfrac{7}{2}\)
=7/2
\((3x-2).(3x+2)-4x.(2x+3)-(2x-1)^2\)
\(=(3x)^2-2^2-8x^2-12x-[(2x)^2-2.2x.1+1^2]\)
\(=9x^2-4-8x^2-12x-4x^2+4x-1\)
\(=(9x^2-8x^2-4x^2)+(4x-12x)-(4+1)\)
\(=-3x^2-8x-5\)
\((x+2).(x^2+3x+1)-(x+1).(x^2-x+1)+(x-2)^3\)
\(=x^3+3x^2+x+2x^2+6x+2-(x^3-1^3)+(x^3-3x^2.2+3x.2^2-2^3)\)
\(=x^3+3x^2+x+2x^2+6x+2-x^3-1+x^3-6x^2+12x-8\)
\(=(x^3-x^3+x^3)+(3x^2+2x^2-6x^2)+(x+6x+12x)+(2-1-8)\)
\(=x^3-x^2+19x-7\)