tính nhanh
a, 69 mũ 2 - 31 mũ 2
b, 1023 mũ 2 - 23 mũ 2
c, 27 mũ 2 + 73 mũ 2 + 54.73
d, 63 mũ 2 + 13 mũ 2 - 26 . 63
e, 25 mũ 2 - 15 mũ 2
i, 87 mũ 2 + 73 mũ 2- 27 mũ 2 - 13 mũ 2
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a)\(6x-9-x^2\)
\(=-\left(x^2+6x+9\right)\)
\(=-\left(x+3\right)^2\)
b)\(x^2+4y^2+4xy\)
\(=\left(x+2y\right)^2\)
c)\(x^2+8x+16\)
\(=\left(x+4\right)^2\)
d)\(9x^2-12xy+4y^2\)
\(=\left(3x-2y\right)^2\)
e)\(-25x^2y^2+10xy-1\)
\(=-\left(25x^2y^2-10xy+1\right)\)
\(=-\left(5xy-1\right)^2\)
f)\(4x^2-4x+1\)
\(=\left(2x-1\right)^2\)
j)\(x^2+6x+9\)
\(=\left(x+3\right)^2\)
h)\(9x^2-6x+1\)
\(=\left(3x-1\right)^2\)
#H
a, 6x - 9 - x2 = - x2 + 6x - 9 = - (x2 - 6x + 9) = - (x - 3)2
b, x2 + 4y2 + 4xy = x2 + 2. x . 2y + (2y)2 = (x + 2y)2
c, x2 + 8x + 16 = x2 + 2 . x . 4 + 42 = (x + 4)2
d, 9x2 - 12xy + 4y2 = (3x)2 - 2 . 3x . 2y + (2y)2 = (3x - 2y)2
e, - 25x2y2 + 10xy - 1 = - (25x2y2 - 10xy + 1) = - [(5xy)2 - 2 . 5xy + 1] = - (5xy - 1)2
f, 4x2 - 4x + 1 = (2x)2 - 2 . 2x + 1 = (2x - 1)2
j, x2 + 6x + 9 = x2 + 2 . x . 3 + 32 = (x + 3)2
h, 9x2 - 6x + 1 = (3x)2 - 2 . 3x + 1 = (3x - 1)2
a) \(81-\left(3x+2\right)^2=9^2-\left(3x+2\right)^2=\left(9-3x-2\right)\left(9+3x+2\right)=\left(7-3x\right)\left(11+3x\right)\)
b) \(\left(7x-4\right)^2-\left(2x+1\right)^2=\left(7x-4-2x-1\right)\left(7x-4+2x+1\right)\)
\(=\left(5x-5\right)\left(9x-3\right)=15\left(x-1\right)\left(3x-1\right)\)
c) \(9\left(x-5y\right)^2-16\left(x+y\right)^2=\left[3\left(x-5y\right)-4\left(x+y\right)\right]\left[3\left(x-5y\right)+4\left(x+y\right)\right]\)
\(=\left(-x-19y\right)\left(7x-11y\right)\)
a, \(\left(2x-1\right)^2-\left(3x-1\right)^2=\left(2x-1-3x+1\right)\left(2x-1+3x-1\right)=-x\left(5x-2\right)\)
b, \(\left(x+1\right)^2-9=\left(x+1-3\right)\left(x+1+3\right)=\left(x-2\right)\left(x+4\right)\)
c, \(\left(4x-1\right)^2-9x^2=\left(4x-1-3x\right)\left(4x-1+3x\right)=\left(x-1\right)\left(7x-1\right)\)
d, \(x^2-9=\left(x-3\right)\left(x+3\right)\); e, \(x^2-25=\left(x-5\right)\left(x+5\right)\)
f, \(\left(x+2\right)^2-\left(3x-1\right)^2=\left(x+2-3x+1\right)\left(x+2+3x-1\right)=\left(-2x+3\right)\left(4x+1\right)\)
i, \(x^6-y^4=\left(x^3\right)^2-\left(y^2\right)^2=\left(x^3-y^2\right)\left(x^3+y^2\right)\)
a)\(69^2-31^2=\left(69-31\right)\left(69+31\right)=38.100=3800\)
\(1023^2-23^2=\left(1023-23\right)\left(1023+23\right)=1000.1046=1046000\)