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2)Tính nhanh:
a)\(202^2-54^2+256.352\)
\(=\left(202-54\right)\left(202+54\right)+256.352\)
\(=148.256+256.352\)
\(=256\left(148+352\right)\)
\(=256.500\)
\(=128000\)
b)\(621^2-769.373-148^2\)
\(=621^2-148^2-769.373\)
\(=\left(621-148\right)\left(621+148\right)-769.373\)
\(=473.769-769.373\)
\(=769\left(473-373\right)\)
\(=769.100\)
\(=76900\)
\(a,\left(x-y+4\right)^2-\left(2x+3y-1\right)^2\)
\(=\left(x-y+4-2x-3y+1\right)\left(x-y+4+2x+3y-1\right)\)
\(=\left(-x-4y+5\right)\left(3x+2y+3\right)\)
\(b,9x^2+90x+225-\left(x-7\right)^2\)
\(=9\left(x^2+10x+25\right)-\left(x-7\right)^2\)
\(=9\left(x+5\right)^2-\left(x-7\right)^2\)
\(=\left[3\left(x+5\right)\right]^2-\left(x-7\right)^2\)
\(=\left(3x+15\right)^2-\left(x-7\right)^2\)
\(=\left(3x+15-x+7\right)\left(3x+15+x-7\right)\)
\(=\left(2x+22\right)\left(4x+8\right)\)
\(=2\left(x+11\right).4\left(x+2\right)\)
\(=8\left(x+2\right)\left(x+11\right)\)
\(c,49\left(y-4\right)^2-9y^2-36y-36\)
\(=\left\{\left[7\left(y-4\right)\right]^2-\left(3y\right)^2\right\}-\left(36y+36\right)\)
\(=\left(7y-28-3y\right)\left(7y-28+3y\right)-36\left(y+1\right)\)
\(=\left(4y-28\right)\left(10y-28\right)-36\left(y+1\right)\)
\(=4\left(y-7\right)2\left(5y-14\right)-36\left(y+1\right)\)
\(=8\left(y-7\right)\left(5y-14\right)-36\left(y+1\right)\)
\(=4\left[2\left(y-7\right)\left(5y-14\right)-9\left(y+1\right)\right]\)
mk ko chắc là câu này mk lm đg
\(d,x^2-5x-14\)
\(=x^2+2x-7x-14\)
\(=x\left(x+2\right)-\left(7x+14\right)\)
\(=x\left(x+2\right)-7\left(x+2\right)\)
\(=\left(x+2\right)\left(x-7\right)\)
\(\left(x-y+4\right)^2-\left(2x+3y-1\right)^2\)
\(=\left(x-y+4+2x+3y-1\right)\left(x-y+4-2x-3y+1\right)\)
\(=\left(3x+2y+3\right)\left(-x-4y+5\right)\)
\(49\left(y-4\right)^2-9y^2-36y-36\)
\(=49\left(y-4\right)^2-\left(9y^2+36y+36\right)\)
\(=49\left(y-4\right)^2-\left(3y+6\right)^2\)
\(=[7\left(y-4\right)]^2-\left(3y+6\right)^2\)
\(=\left(7y-28\right)^2-\left(3y+6\right)^2\)
\(=\left(7y-28+3y+6\right)\left(7y-28-3y-6\right)\)
\(=\left(10y-22\right)\left(4y-34\right)\)
\(b,9x^2+90x+225-\left(x-y\right)^2\)
\(=\left(3x+15\right)^2-\left(x-y\right)^2\)
\(=\left(3x+15-x+y\right)\left(3x+15+x-y\right)\)
\(=\left(2x+y+15\right)\left(4x-y+15\right)\)
a) Ta có: \(\left(x^2+1\right)^2-6\left(x^2+1\right)+9\)
\(=\left(x^2+1\right)^2-2\cdot\left(x^2+1\right)\cdot3+3^2\)
\(=\left(x^2+1-3\right)^2\)
\(=\left(x^2-2\right)^2\)
b) Ta có: \(16\left(x+1\right)^2-25\left(2x+3\right)^2\)
\(=\left[4\left(x+1\right)\right]^2-\left[5\left(2x+3\right)\right]^2\)
\(=\left(4x+4\right)^2-\left(10x+15\right)^2\)
\(=\left(4x+4-10x-15\right)\left(4x+4+10x+15\right)\)
\(=\left(-6x-11\right)\left(14x+19\right)\)
c) Ta có: \(x^{16}-1\)
\(=\left(x^8+1\right)\left(x^8-1\right)\)
\(=\left(x^4-1\right)\left(x^4+1\right)\left(x^8+1\right)\)
\(=\left(x^2-1\right)\left(x^2+1\right)\left(x^4+1\right)\left(x^8+1\right)\)
\(=\left(x-1\right)\left(x+1\right)\left(x^2+1\right)\left(x^4+1\right)\left(x^8+1\right)\)
d) Ta có: \(49\left(x+y\right)^2-36\left(2x+3y\right)^2\)
\(=\left[7\left(x+y\right)\right]^2-\left[6\left(2x+3y\right)\right]^2\)
\(=\left(7x+7y\right)^2-\left(12x+18y\right)^2\)
\(=\left(7x+7y-12x-18y\right)\left(7x+7y+12x+18y\right)\)
\(=\left(-5x-11y\right)\left(19x+25y\right)\)
e) Ta có: \(\left(x+y\right)^2-2\left(x+y\right)+1\)
\(=\left(x+y\right)^2-2\cdot\left(x+y\right)\cdot1+1^2\)
\(=\left(x+y-1\right)^2\)
f) Ta có: \(x^6-8\)
\(=\left(x^2\right)^3-2^3\)
\(=\left(x^2-2\right)\left(x^4+2x^2+4\right)\)
Ta có :
\(1)\left(x^2+y^2-5\right)-4x^2y^2-16xy-16\)
\(=\left(x^2+y^2-5\right)^2-[\left(2xy\right)^2+2.2xy.4+4^2]\)
\(=\left(x^2+y^2-5\right)^2-\left(2xy+4\right)^2\)
\(=\left(x^2+y^2-5-2xy-4\right)\left(x^2+y^2-5+2xy+4\right)\)
\(=\left(x^2+y^2-2xy-9\right)\left(x^2+y^2+2xy-1\right)\)
\(=\left[\left(x-y\right)^2-3^2\right]\left[\left(x+y\right)^2-1\right]\)
\(=\left(x-y+3\right)\left(x-y-3\right)\left(x+y-1\right)\left(x+y+1\right)\)
\(2)x^2y^2\left(y-x\right)+y^2z^2\left(z-y\right)-z^2x^2\left(z-x\right)\)
\(=x^2y^2\left(y-z+z-x\right)+y^2z^2\left(z-y\right)-z^2x^2\left(z-x\right)\)
\(=x^2y^2\left(y-z\right)+x^2y^2\left(z-x\right)+y^2z^2\left(z-y\right)-z^2x^2\left(z-x\right)\)
\(=\left(y-z\right)\left(x^2y^2-y^2z^2\right)+\left(z-x\right)\left(x^2y^2-z^2x^2\right)\)
\(=\left(y-z\right)\left(xy-yz\right)\left(xy+yz\right)+\left(z-x\right)\left(xy-zx\right)\left(xy+xz\right)\)
\(=y^2\left(y-z\right)\left(x-z\right)\left(x+z\right)+x^2\left(z-x\right)\left(y-z\right)\left(y+z\right)\)
\(=\left(y-z\right)\left(x-z\right)[y^2\left(x+z\right)-x^2\left(y+z\right)]\)
\(=\left(y-z\right)\left(x-z\right)(y^2x+y^2z-x^2y-x^2z)\)
\(=\left(y-z\right)\left(x-z\right)[(y^2x-x^2y)+(y^2z-x^2z)]\)
\(=\left(y-z\right)\left(x-z\right)[xy(y-x)+z(y^2-x^2)]\)
\(=\left(y-z\right)\left(x-z\right)[xy(y-x)+z(y-x)\left(x+y\right)]\)
\(=\left(y-z\right)\left(x-z\right)(y-x)\left(xy+xz+yz\right)\)
B1:
a) \(9x^2+90x+225-\left(x-7\right)^2\)
= \(9x^2+90x+225-x^2+14x-49\)
= \(8x^2+104x+176\)
= \(\left(x+2\right)\left(x+11\right)\)
b) \(49\left(y-4\right)^2-9y^2-36y+36\)
= \(49\left(y^2-8y+16\right)-9y^2-36y+36\)
= \(49y^2-392y+784-9y^2-36y+36\)
= \(40y^2-428y+820\)
= \(\left(5y-41\right)\left(8y-20\right)\)
B2:
a) A = \(xy-4y-5y+20=xy-9y+20\)
A = \(y\left(x-9\right)+20\)
Với x = 14, y = \(\dfrac{11}{2}\)
A = \(\dfrac{11}{2}\left(14-9\right)+20=47,5\)
b) B = \(x^2+xy-5x-5y\)
B = \(x\left(x+y\right)-5\left(x+y\right)=\left(x+y\right)\left(x-5\right)\)
Với x = -5, y = -8
B = \(\left(-5-8\right)\left(-5-5\right)=130\)
B3:
a) \(4x^2-25-\left(2x-5\right)\left(2x+7\right)=0\)
\(\left(2x-5\right)\left(2x+5\right)-\left(2x-5\right)\left(2x+7\right)=0\)
\(\left(2x-5\right)\left(2x+5-2x-7\right)=0\)
\(\left(2x-5\right)\left(-2\right)=0\)
\(x=\dfrac{5}{2}\)
b) \(\left(x^3+27\right)+\left(x+3\right)\left(x-9\right)=0\)
\(\left(x+3\right)\left(x^2-3x+9\right)+\left(x+3\right)\left(x-9\right)=0\)
\(\left(x+3\right)\left(x^2-3x+9+x-9\right)=0\)
\(\left(x+3\right)x\left(x-2\right)=0\)
\(\left[{}\begin{matrix}x=-3\\x=0\\x=2\end{matrix}\right.\)
c) \(\left(2x^3+2x^2\right)+\left(3x^2+3\right)=0\)
\(2x^3+5x^2+3=0\)
\(\Rightarrow\) Đề sai rồi, nghiệm khủng bố lắm.
dễ vãi lol ra bn ngu vãi đái
a, \(\left(x-y+4\right)^2-\left(2x+3y-1\right)^2=\left(x-y+4+2x+3y-1\right)\left(x-y+4-2x-3y+1\right)\)
\(=\left(3x+2y+3\right)\left(-x-4y+5\right)\)
b, \(x^6+y^6=\left(x^2\right)^3+\left(y^2\right)^3=\left(x^2+y^2\right)\left(x^4-x^2y^2+y^4\right)\)
c, \(x^{16}-1=\left(x^2\right)^8-1=\left[\left(x^2\right)^4\right]^2-1=\left(x^8-1\right)\left(x^8+1\right)\)
Phân tích à :)
a) ( x - y + 4 )2 - ( 2x + 3y - 1 )2
= [ ( x - y + 4 ) - ( 2x + 3y - 1 ) ][ ( x - y + 4 ) + ( 2x + 3y - 1 ) ]
= ( x - y + 4 - 2x - 3y + 1 )( x - y + 4 + 2x + 3y - 1 )
= ( -x - 4y + 5 )( 3x + 2y + 3 )
b) x6 + y6 = ( x2 )3 + ( y2 )3 = ( x2 + y2 )( x4 - x2y2 + y4 )
c) x16 - 1 = ( x8 )2 - 12 = ( x8 - 1 )( x8 + 1 )
= ( x4 - 1 )( x4 + 1 )( x8 + 1 )
= ( x2 - 1 )( x2 + 1 )( x4 + 1 )( x8 + 1 )
= ( x - 1 )( x + 1 )( x2 + 1 )( x4 + 1 )( x8 + 1 )
d) x36 - 64 = ( x18 )2 - 82
= ( x18 - 8 )( x18 + 8 )
= ( x6 - 2 )( x12 + 2x + 4 )( x6 + 2 )( x12 - 2x + 4 )
e) 9x2 + 90x + 225 - ( x - 7 )2
= ( 3x + 15 )2 - ( x - 7 )2
= ( 3x + 15 - x + 7 )( 3x + 15 + x - 7 )
= ( 2x + 22 )( 2x - 8 )
= 2( x + 11 ).2( x - 4 )
= 4( x + 11 )( x - 4 )
f) 49( y - 4 )2 - 9y2 - 36y - 36
= 72( y - 4 )2 - ( 9y2 + 36y + 36 )
= ( 7y - 28 )2 - ( 3y + 6 )2
= ( 7y - 28 - 3y - 6 )( 7y - 28 + 3y + 6 )
= ( 4y - 34 )( 10y - 22 )
= 2( 2y - 17 ).2( 5y - 11 )
= 4( 2y - 17 )( 5y - 11 )