[tex] w^{2} + 8w + 16 [/tex]
when we compare the given equation to [tex] ax^{2} + bx + c [/tex]
a=1, b=8,c=16
So, ac=1*16=16 and b=8
We need factor pair of ac, 16, which sum upto b, 8.
As, 4*4=16 and 4+4=8
4 and 4 are required factor pair.
[tex] w^{2} + 4w+4w + 16 [/tex]
[tex] w(w+4) + 4(w+4) [/tex]
[tex] (w+4)(w+4) [/tex]
[tex] (w+4)^{2} [/tex]
So,[tex] w^{2} + 8w + 16 [/tex]=[tex] (w+4)^{2} [/tex]
[tex] 3y^{2} + 10y + 7 [/tex]
when we compare the given equation to [tex] ax^{2} + bx + c [/tex]
a=3, b=10,c=7
So, ac=3*7=21 and b=10
We need factor pair of ac, 21, which sum upto b, 10.
As, 3*7=21 and 3+7=10
3 and 7 are required factor pair.
[tex] 3y^{2} + 3y+7y + 7 [/tex]
[tex] 3y(y+1)+7(y+1) [/tex]
[tex] (3y+7)(y+1) [/tex]
[tex] 3y^{2} + 10y + 7 [/tex]=[tex] (3y+7)(y+1) [/tex]
