How would I simplify each of these Algebraic Expressions?

1. ?
2. (xsquared-25)
3. (6xsquared+8x)

1. Multiply this by -1 so that the coefficient of x^2 will be positive.  Then add the two quadradics.  I believe you can factor out a 2 and possibly factor what is left.

2.  This is a sum of difference of squares.  Check your book for the format of the quadradic given the factors.

3.  This is a straightforward multiplication by FOIL.

By using combining like terms. When there is several number times x^2's, add them with respect to the sign in front of them; when there is two or more number times x's, add them with respect to the sign, etc...

1.) x^2-4x+7-(3x^2-8x+7)= x^2-4x+7-3x^2+8x-7

                                  =  x^2-3x^2+8x-4x+7-7
                                  = -2x^2+4x+0
                                  = -2x^2+4x  answer

2.) Use the Distributive property distributing each number of the first factor (x-5)onto each number of the second factor:

=x^2+5x-5x-25
=x^2-25          answer

3.) same process as 2.)