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a) \(x^2-6x-y^2-4y+5=x^2-6x+9-y^2-4y-4\)
\(=\left(x^2-6x+9\right)-\left(y^2+4y+4\right)=\left(x-3\right)^2-\left(y+2\right)^2\)
b) \(4a^2-12a-b^2+2b+8=4a^2-12a+9-b^2+2b-1\)
\(=\left(4a^2-12a+9\right)-\left(b^2-2b+1\right)=\left(2a-3\right)^2-\left(b-1\right)^2\)
x2 - 6x - y2 - 4y + 5
= ( x2 - 6x + 9 ) - ( y2 + 4y + 4 )
= ( x - 3 )2 - ( y + 2 )2
4a2 - 12a - b2 + 2b + 8
= ( 4a2 - 12a + 9 ) - ( b2 - 2b + 1 )
= ( 2a - 3 )2 - ( b - 1 )2
a)x2-6x+9
=x2-2.x.3+32
=(x-3)2
b)4x2+4x+1
=(2x)2+2.2x.1+12
=(2x+1)2
c)4x2+12xy+9y2
=(2x)2+2.2x.3y+(3y)2
=(2x+3y)2
d)4x4-4x2+4
=(2x2)2-2.2x2.2+22
=(2x2-2)2
\(x^2-2xy+5y^2+4y+1\)
\(=x^2-2xy+y^2+4y^2+4y+1\)
\(=\left(x^2-2xy+y^2\right)+\left(4y^2+4y+1\right)\)
\(=\left(x-y\right)^2+\left(2y+1\right)^2\)
\(x^2-2xy+5y^2+4y+1=x^2-2xy+y^2+4y^2+4y+1=\left(x-y\right)^2+\left(2y+1\right)^2\)
a) ( x + 1 ) 2 . b) ( x – 4 ) 2 .
c) x 2 4 + x + 1 ; d) ( 2 x – 2 y ) 2 .
a) ( 2 x + 1 ) 2 . b) ( 3 x – 2 ) 2 .
c) 1 2 ab 2 + 1 2 . d) ( 4 uv 2 – 1 ) 2 .
\(A=\left(x-1\right)\left(x+1\right)=x^2-1\)
\(B=\left(x-2y\right)\left(x+2y\right)=x^2-4y^2\)
\(C=\left(3x^2-2y\right)\left(3x^2+2y\right)=9x^4-4y^2\)