Rút gọn biểu thức: \(\left(2x-5\right)\left(4x^2+10x+25\right)\left(2x+5\right)\left(4x^2-10x+25\right)-^4\)\(64x^4\)
Rút gọn biểu thức:
\(\left(x+3\right)^2+\left(2x+1\right)\left(3x-5\right)-2x\left(3-x\right)+4x+25\)
\(57)\left(2x+5\right)\left(4x^2-10x+25\right)\)
\(59)\left(2x+3y\right)\left(4x^2-6xy+9y^2\right)\)
\(a,\left(2x+5\right)\left(4x^2-10x+25\right)\)
\(=\left(2x+5\right)\left[\left(2x\right)^2-2x.5+5^2\right]\)
\(=\left(2x\right)^3+5^3=8x^3+125\)
\(b,\left(2x+3y\right)\left(4x^2-6xy+9y^2\right)\)
\(=\left(2x+3y\right)\left[\left(2x\right)^2-2x.3y+\left(3y\right)^2\right]\)
\(=\left(2x\right)^3+\left(3y\right)^3=8x^3+27y^3\)
57) (2x + 5)(4x2 - 10x + 25)
= 2x.4x2 + 2x.(-10x) + 2x.25 + 5.4x2 + 5.(-10x) + 5.25
= 8x3 - 20x2 + 50x + 20x2 - 50x + 125
= 8x3 + (-20x2 + 20x2) + (50x - 50x) + 125
= 8x3 + 125
59) làm tương tự
A.tính
\(25x^2-10x+1\)
B.rút gọn
\(\left(x-2\right).\left(x^2+2x+4\right)-6x^2+12x\)
(2x+5) .(5-2x)+(x-5).(5+4x)
B: rút gọn
a) Ta có: \(\left(x-2\right)\left(x^2+2x+4\right)-6x^2+12x\)
\(=x^3-6x^2+12x-8\)
\(=\left(x-2\right)^3\)
b) Ta có: \(\left(2x+5\right)\left(5-2x\right)+\left(x-5\right)\left(4x+5\right)\)
\(=25-4x^2+4x^2+5x-20x-25\)
=-15x
Thu gọn biểu thức :
1, \(\left(x+5\right)\cdot\left(x^2-5x+25\right)-\left(x-2\right)\cdot\left(x^2+2x+4\right)\)
2, \(\left(2x-3\right)\cdot\left(4x^2+6x+9\right)-\left(2x+1\right)^3\)
1. \(\left(x+5\right)\left(x^2-5x+25\right)-\left(x-2\right)\left(x^2+2x+4\right)\)
\(=x^3+125-\left(x^3-8\right)=x^3+125-x^3+8=133\)
1,
\(\left(x+5\right)\left(x^2-5x+25\right)-\left(x-2\right)\left(x^2+2x+4\right)\\ =\left(x^3+5^3\right)-\left(x^3-2^3\right)\\ =x^3+125-x^3+8\\ =\left(x^3-x^3\right)+\left(125+8\right)\\ =133\)
b,
\(\left(2x-3\right)\left(4x^2+6x+9\right)-\left(2x+1\right)^3\\ =\left[\left(2x\right)^3-3^3\right]-\left[\left(2x\right)^3+3\cdot\left(2x\right)^2\cdot1+3\cdot2x+1+1\right]\\ =\left(8x^3-27\right)-\left(8x^3+12x^2+6x+1\right)\\ =8x^3-27-8x^3-12x^2-6x-1\\ =\left(8x^3-8x^3\right)-\left(12x^2+6x\right)-\left(27+1\right)\\ =-6x\left(2x+1\right)-28\\ =\left(-2\right)\left[3x\left(2x+1\right)+14\right]\)
rút gọn các biểu thức sau
a, \(\left(2x+1\right)^2+2\left(4x^2-1\right)+\left(2x-1\right)^2\)
b, \(\left(x^2-1\right)\left(x+2\right)-\left(x-2\right)\left(x^2+2x+4\right)\)
a: \(\left(2x+1\right)^2+2\left(4x^2-1\right)+\left(2x-1\right)^2\)
\(=\left(2x+1\right)^2+2\left(2x+1\right)\left(2x-1\right)+\left(2x-1\right)^2\)
\(=\left(2x+1+2x-1\right)^2=\left(4x\right)^2=16x^2\)
b: \(\left(x^2-1\right)\left(x+2\right)-\left(x-2\right)\left(x^2+2x+4\right)\)
\(=x^3+2x^2-x-2-x^3+8\)
\(=2x^2-x+6\)
a) \(\left(2x+1\right)^2+2\left(4x^2-1\right)+\left(2x-1\right)^2\)
\(=\left(2x+1\right)^2+2\left(2x+1\right)\left(2x-1\right)+\left(2x-1\right)^2\)
\(=\left[\left(2x+1\right)+\left(2x-1\right)\right]^2\)
\(=\left(2x+1+2x-1\right)^2\)
\(=\left(4x\right)^2\)
\(=16x^2\)
b) \(\left(x^2-1\right)\left(x+2\right)-\left(x-2\right)\left(x^2+2x+4\right)\)
\(=\left(x^3+2x^2-x-2\right)-\left(x^3-8\right)\)
\(=x^3+2x^2-x-2-x^3+8\)
\(=2x^2-x+6\)
\(a,\left(2x+1\right)^2+2\left(4x^2-1\right)+\left(2x-1\right)^2\)
\(=\left(2x+1\right)^2+2\cdot\left[\left(2x\right)^2-1^2\right]+\left(2x-1\right)^2\)
\(=\left(2x+1\right)^2+2\cdot\left(2x+1\right)\cdot\left(2x-1\right)+\left(2x-1\right)^2\)
\(=\left[\left(2x+1\right)+\left(2x-1\right)\right]^2\)
\(=\left(2x+1+2x-1\right)^2\)
\(=\left(4x\right)^2\)
\(=16x^2\)
\(---\)
\(b,\left(x^2-1\right)\left(x+2\right)-\left(x-2\right)\left(x^2+2x+4\right)\)
\(=x^2\left(x+2\right)-\left(x+2\right)-\left(x^3-2^3\right)\)
\(=x^3+2x^2-x-2-x^3+8\)
\(=2x^2-x+6\)
Rút gọn biểu thức
A = \(\left(x-2\right)\left(x^2+2x+4\right)-x\left(x^2-2\right)\)
B = \(\left(x-3\right)\left(x+2\right)-\left(2x^3-2x^2-10x\right):2x\)
Tính
a)\(\left(x^4+2x^3+10x-25\right):\left(x^2+5\right)\)
b) \(\left(3x^4-8x^3-10x^2+8x-5\right):\left(3x^2-2x+1\right)\)
a) \(\left(x^4+2x^3+10x-25\right):\left(x^2+5\right)\)
\(=\left[\left(2x^3+10x\right)+\left(x^4-25\right)\right]:\left(x^2+5\right)\)
\(=\left[2x\left(x^2+5\right)+\left(x^2-5\right)\left(x^2+5\right)\right]:\left(x^2+5\right)\)
\(=\left(x^2+5\right)\left(x^2+2x-5\right):\left(x^2+5\right)\)
\(=x^2+2x-5\)
Rút gọn biểu thức :
\(H=\left(2x-y+5^2\right)+\left(4x-2y+10\right)\left(y-2x\right)+\left(2x-y\right)^2\)
H=(2x-y+10)+(4xy-8x^2-2y^2-4xy+10y+20x)+(4x-y)
H=(2x-y+10)+(4xy-16x-4y-4xy+10y+20x)+(4x-y)
H=(2x-y+10)+(4x+6y)+(4x-y)
H=2x-y+10+4x+6y+4x-y
H=10x+4y+10
Thu gọn biểu thức
1,\(\left(x-2\right)^3-\left(2x+3\right)^3-7\cdot\left(1-x\right)^3\)
2,\(\left(x+5\right)\cdot\left(x^2-5x+25\right)-\left(x-2\right)\cdot\left(x^2+2x+4\right)\)
3, \(\left(2x-3\right)\cdot\left(4x^2+6x+9\right)-\left(2x+1\right)^3\)
1: \(=x^3-6x^2+12x-8-8x^3-36x^2-54x-27+7\left(x-1\right)^3\)
\(=-7x^3-42x^2-42x-35+7x^3-21x^2+21x-7\)
\(=-63x^2-21x-42\)
2: \(=x^3+125-\left(x^3-8\right)=125+8=133\)
3: \(=8x^3-27-8x^3-12x^2-6x-1=-12x^2-6x-28\)