`1)`
`a)-2xy.5x^2y^3`
`=-10x^3y^4`
`b)2x(3x^2-4x+5)`
`=6x^3-8x^2+10x`
`c)(x+3)(x^2+3x-5)`
`=x^3+3x^2-5x+3x^2+9x-15`
`=x^3+6x^2+4x-15`
`2)`
`a)97^2-9`
`=97^2-3^2`
`=(97-3)(97+3)`
`=94.100`
`=9400`
`b)(x+2)^2-(x-2)(x+2)=0`
`⇒(x+2)^2-(x^2-2^2)=0`
`⇒x^2+4x+4-x^2+4=0`
`⇒4x+8=0`
`⇒4x=-8`
`⇒x=-2`
`3)`
`a)6x^2y-12xy^2`
`=6xy(x-2y)`
`b)x^2y-x+5xy-5`
`=(x^2y-x)+(5xy-5)`
`=x(xy-1)+5(xy-1)`
`=(x+5)(xy-1)`
`c)x^2-16+2xy+y^2`
`=(x^2+2xy+y^2)-4^2`
`=(x+y)^2-4^2`
`=(x+y+4)(x+y-4)`
`4)`
`a)(3x^2-6x):3x`
`=x-2`
`b)(x^4-x^3-3x^2+x+2):(x^2-1)`
`=x^2-x-2`
