3,
`4+8a+4a^2`
`=4(1+2a+a^2)`
`=4(1+a)^2`
4,
`25+a^2+10a`
`=a^2+2.a.5+5^2`
`=(a+5)^2`
5,
`x^2-2xy+y^2`
`=(x-y)^2`
6,
`4-4y+y^2`
`=2^2-2.2.y+y^2`
`=(2-y)^2`
7,
`25+4x^2-20x`
`=(2x)^2-2.2x.5+5^2`
`=(2x-5)^2`
8,
`9x^2-6x+1`
`=(3x)^2-2.3x.1+1^2`
`=(3x-1)^2`
9,
`25a^2+4b^2-20ab`
`=(5a)^2-2.5a.2b+(2b)^2`
`=(5a-2b)^2`
10,
`4a^2-12ab+9b^2`
`=(2a)^2-2.2a.3b+(3b)^2`
`=(2a-3b)^2`
11,
`4x^2+9+12x`
`=(2x)^2+2.2x.3+3^2`
`=(2x+3)^2`
12,
`16a^2+9-24a`
`=(4a)^2-2.4a.3+3^2`
`=(4a-3)^2`
13,
`25+4x^2-20x`
`=(2x)^2-2.2x.5+5^2`
`=(2x-5)^2`
14,
`x^2+6xy+9y^2`
`=x^2+2.x.3y+(3y)^2`
`=(x+3y)^2`
$\\$
$\\$
1,
`x^2-y^2=(x-y)(x+y)`
2,
`x^2-9=x^2-3^2=(x-3)(x+3)`
3,
`4x^2-1=(2x)^2-1^2=(2x-1)(2x+1)`
4,
`16-x^4`
`=4^2-(x^2)^2`
`=(4-x^2)(4+x^2)`
`=(2^2-x^2)(4+x^2)`
`=(2-x)(2+x)(4+x^2)`
5,
`4y^2-4x^2=4(y^2-x^2)=4(y-x)(y+x)`
6,
`16a^2-9y^2=(4a)^2-(3y)^2=(4a-3y)(4a+3y)`
7,
`81-4y^2=9^2-(2y)^2=(9-2y)(9+2y)`
8,
`-9+4x^2=4x^2-9=(2x)^2-3^2=(2x-3)(2x+3)`
9,
`1-25a^4=1^2-(5a^2)^2=(1-5a^2)(1+5a^2)`
