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a. Ta có: x2 – y2 = (x + y)(x – y)
b. Thay x = 87, y = 13, ta được:
x2 – y2 = (x + y)(x – y)
= (87 + 13)(87 – 13)
= 100.74 = 7400
c. Ta có: x3 + 9x2 + 27x + 27
= x3 + 3.x2.3 + 3.x.32 + 33
= (x + 3)3
Thay x = 97, ta được: (x + 3)3 = (97 + 3)3 = 1003 = 1000000
\(a,=\left(x+3\right)^3=\left(7+3\right)^3=10^3=1000\\ b,=\left(4-x\right)^3=\left(4-24\right)^3=\left(-20\right)^3=-8000\\ c,=\left(x-1\right)^3=\left(11-1\right)^3=10^3=1000\)
a,x3+3x2+3x+1
b,x2+6x+9
c,-x3+9x2-27x+27
d,x2+4x+4
k,10x-25-x2
f,(x+y)2-9x2
g,8x3+42x2y+16xy2+6xy+y3
a) \(x^3+3x^2+3x+1=x^2+3\cdot x^2\cdot1+3\cdot x\cdot1^2+1^3=\left(x-1\right)^3\)
b) \(x^2+6x+9=x^2+2\cdot3\cdot x+3^2=\left(x+3\right)^2\)
c) \(-x^3+9x^2-27x+27\)
\(=-\left(x^3-9x^2+27x-27\right)\)
\(=-\left(x^3-3\cdot3\cdot x^2+3\cdot3^2\cdot x-3^3\right)=-\left(x-3\right)^3\)
d) \(x^2+4x+4=x^2+2\cdot2\cdot x+2^2=\left(x+2\right)^2\)
k) \(10x-25-x^2=-x^2+10x-25=-\left(x^2-10x+25\right)\)
\(=-\left(x^2-2\cdot5\cdot x+5^2\right)=-\left(x-5\right)^2\)
f) \(\left(x+y\right)^2-9x^2=\left(x-y\right)^2-\left(3x\right)^2=\left[\left(x-y\right)-3x\right]\left[\left(x-y\right)+3x\right]\)
\(=\left(x-y-3x\right)\left(x-y+3x\right)=\left(-2x-y\right)\left(4x-y\right)\)
a: \(\left(2x-1\right)^2-2\left(2x-3\right)^2+4\)
\(=4x^2-4x+1+4-2\left(4x^2-12x+9\right)\)
\(=4x^2-4x+5-8x^2+24x-18\)
\(=-4x^2+20x-13\)
e: \(\left(2x+3y\right)\left(4x^2-6xy+9y^2\right)=8x^3+27y^3\)
a: Ta có: \(\left(2x-1\right)^2-2\left(2x-3\right)^2+4\)
\(=4x^2-4x+1-2\left(4x^2-12x+9\right)+4\)
\(=4x^2-4x+5-8x^2+24x-18\)
\(=-4x^2+20x-13\)
b: \(\left(3x+2\right)^2+2\left(3x+2\right)\left(1-2y\right)+\left(1-2y\right)^2\)
\(=\left(3x+2+1-2y\right)^2\)
\(=\left(3x-2y+3\right)^2\)
\(a,=\left(x+3\right)^3=\left(-3+3\right)^3=0\\ b,=27x^3+1-\left(1-27x^3\right)=27x^3+1-1+27x^3=54x^3\\ =54\cdot10^3=54\cdot1000=54000\)
c, hình như sai đề á e
a) x2 - y2 = (x - y)(x + y)
Tại x = 87 ; y = 13, ta có:
A = (87 - 13)(87 + 13)
= 74. 100
= 7400
b) B = 25x2 - 30x + 9 = (5x - 3)2
Tại x = 2, ta có:
B = (5. 2 - 3)2 = 72 = 49
c) C = 4x2 - 28x + 49 = (2x - 7)2
Tại x = 4, ta có:
(2. 4 - 7)2 = 12 = 1
d) D = x3 - 3x2 + 3x - 1 = (x - 1)3
Tại x = 101, ta có:
(101 - 1)3 = 1003 = 1000000
a) Ta có: \(M=x^2-2xy+y^2-10x+10y\)
\(=\left(x-y\right)^2-10\left(x-y\right)\)
\(=9^2-10\cdot9=-9\)
a) \(x^2-y^2=\left(x-y\right)\left(x+y\right)=\left(87-13\right)\left(87+13\right)=74.100=7400\)
b) \(x^3-3x^2+3x-1=\left(x-1\right)^3=\left(101-1\right)^3=100^3=1000000\)
c) \(x^3+9x^3+27x+27=\left(x+3\right)^3=\left(97+3\right)^3=100^3=1000000\)
d) \(25x^2-30x+9=25.2^2-30.2+9=100-60+9=49\)
d) \(4x^2-28x+49=\left(2x-7\right)^2=\left(2.4-7\right)^2=1^2=1\)
a, \(x^2-y^2=\left(x-y\right)\left(x+y\right)\)
Thay x = 87 ; y = 13 ta được :
\(=\left(87-13\right)\left(87+13\right)=74.100=7400\)
b, \(x^3-3x^2+3x-1=\left(x-1\right)^3\)
Thay x = 101 ta được : \(=\left(101-1\right)^3=100^3=1000000\)
c, \(x^3+9x^2+27x+27=\left(x+3\right)^3\)
Thay x = 97 ta được : \(=\left(97+3\right)^3=100^3=1000000\)
d, \(25x^2-30x+9=\left(5x-3\right)^2\)Thay x = 2 ta được :
\(=\left(10-3\right)^2=7^2=49\)
e, \(4x^2-28x+49=\left(2x-7\right)^2\)
Thay x = 4 ta được : \(=\left(8-7\right)^2=1\)