Rút gọn biểu thức:
a) x.(x-3).(x+3)-(x^2-2).(x^2+2)
b)(y+2).(y-2).(y^2+4)-(y^2-3).(y^2+3)
c) (a-b+c)^2+(b-c)^2+2.(a-b+c).(c-b)
Giúp mình nha :33
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Câu 3:
a: \(49^2=2401\)
b: \(51^2=2601\)
c: \(99\cdot100=9900\)
\(a.\left(3x-1\right)^2+\left(x+3\right)\left(2x-1\right)\)
\(=9x^2-6x+1-2x^2+x-6x+3\)
\(=7x^2-11x+4\)
\(a,=x^3-16x-x^2-1-x^2+1=x^3-2x^2-16x\\ b,=y^4-81-y^4+4=-77\\ d,=a^2+b^2+c^2+2ab-2bc-2ac+a^2-2ac+c^2-2ab-2ac\\ =2a^2+b^2+2c^2-2bc-6ac\)
a) \(=5x^2+40x+80+4\left(x^2-10x+25\right)-9\left(x+4\right)\left(x-4\right)\)
\(=5x^2+40x+80+4x^2-40x+100-9x^2+144\)
\(=9x^2-9x^2+40x-40x+324\)
\(=324\)
b) \(=x^2+4xy+4y^2+4x^2-4xy+y^2-5x^2+5y^2-10y^2+90\)
\(=5x^2-5x^2+10y^2-10y^2+\left(4xy-4xy\right)+90\)
\(=90\)
c)
\(=a^2+b^2+c^2+2\left(ab+bc+ca\right)+a^2+b^2+c^2+2ab-2ac-2bc-2a^2-4ab-2b^2\)
\(=\left(2a^2-2a^2\right)+\left(2b^2-2b^2\right)+2c^2+4ab-4ab+2\left(ac+bc-ac-bc\right)\)
\(=2c^2\)
a) 5( x + 4 )2 + 4( x - 5 )2 - 9( 4 + x )( x - 4 )
= 5( x2 + 8x + 16 ) + 4( x2 - 10x + 25 ) - 9( x2 - 16 )
= 5x2 + 40x + 80 + 4x2 - 40x + 100 - 9x2 + 144
= ( 5x2 + 4x2 - 9x2 ) + ( 40x - 40x ) + ( 80 + 100 + 144 )
= 324
b) ( x + 2y )2 + ( 2x - y )2 - 5( x + y )( x - y ) - 10( y + 3 )( y - 3 )
= x2 + 4xy + 4y2 + 4x2 - 4xy + y2 - 5( x2 - y2 ) - 10( y2 - 9 )
= x2 + 4xy + 4y2 + 4x2 - 4xy + y2 - 5x2 + 5y2 - 10y2 + 90
= ( x2 + 4x2 - 5x2 ) + ( 4xy - 4xy ) + ( 4x2 + y2 + 5y2 - 10y2 ) + 90
= 90
c) ( a + b + c )2 + ( a + b - c )2 - 2( a + b )2
= [ ( a + b ) + c ]2 + [ ( a + b ) - c ]2 - 2( a + b )2
= ( a + b )2 + 2( a + b )c + c2 + ( a + b )2 - 2( a + b )c + c2 - 2( a + b )2
= [ ( a + b )2 + ( a + b )2 - 2( a + b )2 ] + [ 2( a + b )c - 2( a + b )c ] + ( c2 + c2 )
= 2c2
Bài 1:
- a,(2+xy)^2=4+4xy+x^2y^2
- b,(5-3x)^2=25-30x+9x^2
- d,(5x-1)^3=125x^3 - 75x^2 + 15x^2 - 1
a) \(x\left(x-3\right)\left(x+3\right)-\left(x^2-2\right)\left(x^2+2\right)\)
\(=x\left(x^2-9\right)-x^4+4\)
\(=x^3-9x-x^4+4\)
\(=-x^4+x^3-9x+4\)
b) \(\left(y+2\right)\left(y-2\right)\left(y^2+4\right)-\left(y^2-3\right)\left(y^2+3\right)\)
\(=\left(y^2-4\right)\left(y^2+4\right)-y^4+9\)
\(=y^4-16-y^4+9\)
\(=-7\)