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\(a,\left(2x-3y\right)\left(4x^2+6xy+9y^2\right)=8x^3-27y^3\)
\(b,\left(x+3y\right)\left(x^2-3xy+9y^2\right)=x^3+27y^3\)
\(c,64-48x+12x^2-x^3=\left(4-x\right)^3\)
\(d,x^3+6x^2y+12xy^2+8y^3=\left(x+2y\right)^3\)
\(e,8x^3-60x^2y+150xy^2-125y^3=\left(2x-5y\right)^3\)
\(205^2-95^2=\)
\(=\left(205-95\right)\left(205+95\right)\)
\(=200.300\)
\(=60000\)
\(36^2-14^2=\)
\(=\left(36-14\right)\left(36+14\right)\)
\(=22.50\)
\(=1100\)
\(205^2-95^2=\left(205-95\right)\left(205+95\right)=110.300=33000\)
\(36^2-14^2=\left(36-14\right)\left(36+14\right)=22.50=1100\)
\(97^2-3^2=\left(97-3\right)\left(97+3\right)=94.100=9400\)
\(x^2-y^2=\left(x+y\right)\left(x-y\right)\)
\(\left(a+b\right)^2=a^2+2ab+b^2\)
ai k mk mk k lại
a) \(x^2-6x+9=\left(x-3\right)^2\)
b) \(x^2+8x+16=\left(x+4\right)^2\)
c) \(\left(x-3\right)^2-16=\left(x-3-4\right)\left(x-3+4\right)=\left(x-7\right)\left(x+1\right)\)
d) \(64+16x+x^2=\left(x+8\right)^2\)
e) \(x^2-x+\frac{1}{4}=\left(x-\frac{1}{2}\right)^2\)
f) mk chỉnh đề
\(8-36x+54x^2-27x^3=\left(2-3x\right)^3\)
g) \(8x^3+12x^2y+6xy^2+y^3=\left(2x+y\right)^3\)
a) \(\left(x-2\right)^3-\left(x+4\right)^2\)
\(=x^3-6x^2+12x-8-\left(x^2+8x+16\right)\)
\(=x^3-6x^2+12x-8-x^2-8x-16\)
\(=x^3-7x^2+4x-24\)
b) \(\left(x-3\right)^3+\left(x+3\right)^3\)
\(=x^3-9x^2+27x-27+x^3+9x^2+27x+27\)
\(=2x^3+54x\)
\(=2x\left(x^2+27\right)\)
c) \(\left(x-2\right)^2-\left(x+2\right)^2=\left(x^2-4x+4\right)-\left(x^2+4x+4\right)\)
\(=x^2-4x+4-x^2-4x-4=-8x\)
d) \(\frac{x^2-25}{x+5}=\frac{\left(x-5\right)\left(x+5\right)}{x+5}=x-5\)
e) \(\frac{x^3-6x^2+12x-8}{x-2}=\frac{\left(x-2\right)^3}{x-2}=\left(x-2\right)^2\)
g) \(\frac{x^3-125}{x-5}=\frac{x^3-5^3}{x-5}=\frac{\left(x-5\right)\left(x^2+5x+25\right)}{x-5}=x^2+5x+25\)
\(S=1^3+2^3+3^3+...+n^3=\left(1+2+3+...+n\right)^2\)
\(=\left[\dfrac{n\left(n+1\right)}{2}\right]^2=\dfrac{n^2\cdot\left(n+1\right)^2}{4}\)
\(a,\left(2x+y+3\right)^2=4x^2+y^2+9+4xy+12x+6y\)
\(b,\left(x-2y+1\right)^2=x^2+4y^2+1-4xy+2x-4y\)
\(c,\left(x^2-2xy^2-3\right)^2=x^4+2x^2y^4+9-4x^3y^2-6x^2+12xy^2\)
\(27x^3-54x^2y+36xy^2-8y^3\)
\(=\left(3x-2y\right)^3\)
Tại \(x=4;\)\(y=6\) thì gtbt là:
\(\left(3.4-2.6\right)^3=0\)
d) 992 + 1 + 198 = 992 + 2.99.1 + 12 = ( 99 + 1 )2 = 1002 = 10 000
e) 26.34 = ( 30 - 4 )( 30 + 4 ) = 302 - 42 = 900 - 16 = 884
g) 95.105 = ( 100 - 5 )( 100 + 5 ) = 1002 - 52 = 10 000 - 25 = 9975
h) 29.31 = ( 30 - 1 )( 30 + 1 ) = 302 - 12 = 900 - 1 = 899