Given:
[tex]y^{2}(2 y-5)-8 y+20[/tex]
To find:
The product of the expression.
Solution:
[tex]y^{2}(2 y-5)-8 y+20=y^{2}(2 y-5)+(-8 y+20)[/tex]
Take out -4 as a common factor in Last two terms.
[tex]=y^{2}(2 y-5)-4(2 y-5)[/tex]
Make sure the terms in both brackets must be same.
Take out common factor (2y - 5) from both terms.
[tex]=(2 y-5)(y^{2}-4)[/tex]
4 can be written as 2².
[tex]=(2 y-5)\left(y^{2}-2^2\right)[/tex]
Using the identity: [tex](a^2-b^2)=(a-b)(a+b)[/tex]
[tex]=(2 y-5)(y-2)(y+2)[/tex].
The product is [tex](2 y-5)(y-2)(y+2)[/tex].