what is The length of the remaining piece of beam

Question

A wooden beam is (7y²+5y+1) meters long. If a piece of length (y²−12) meters is cut​ off, express the length of the remaining piece of beam as a polynomial in y.

Answer 1

Total length of the bean= (7y^2+5y+1) meters

Length of the bean cut= (y^2-12)

Now, writing this in equation:

(7y^2+5y+1) - (y^2-12)

solution,

= 7y^2+5y+1-y^2-12

=6y^2+5y-11

The answer can be left here but more simplification can also be done.

=6y^2+(11-6)y-11

=6y^2+11y-6y-11

=y(6y+11)-1(6y+11)

=(y-1)(6y+11)

Now,

y=1 and y= -11/6

Answer 2

You would express it as: 7y^2 + 5y + 1 - (y^2 - 12) = 7y^2 + 5y + 1 - y^2 + 12 = 6y^2 + 5y + 13