a) \(x^3+8y^3+4x+8y\)
\(=x^3-2x^2y+4xy^2+4x+2x^2y-4xy^2+8y^3+8y\)
\(=\left(x^3-2x^2y+4xy^2+4x\right)+\left(2x^2y-4x^2y+8y^3+8y\right)\)
\(=x\left(x^2-2xy+4y^2+4\right)+2y\left(x^2-2xy+4y^2+4\right)\)
\(=\left(x^2-2xy+4y^2+4\right)\left(x+2y\right)\)
b) \(x^2+6xy+9y^2+5x+15y\)
\(=\left(x^2+6xy+9y^2\right)+\left(5x+15y\right)\)
\(=\left(x+3y\right)^2+5\left(x+3y\right)\)
\(=\left(x+3y\right)\left(x+3y+5\right)\)
c) \(25-x^2+2xy-y^2\)
\(=25-\left(x^2-2xy+y^2\right)\)
\(=25-\left(x-y\right)^2\)
\(=5^2-\left(x-y\right)^2\)
\(=\left(5+x-y\right)\left(5-x+y\right)\)
`x^3+8y^3 +4x+8y`
`=(x+2y)(x^2 - 2xy + 4y^2 ) +4 (x+2y)`
`= (x+2y) (x^2 -2xy +4y^2 +4)`
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`x^2 +6xy +9y^2 +5x+15y`
`= (x+3y)^2 + 5(x+3y)`
`=(x+3y)( x+3y +5)`
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`25-x^2 +2xy -y^2`
`= 25 - (x^2 -2xy+y^2)`
`=25-(x-y)^2`
`=(5-x+y)(5+x-y)`