Given the equations:
[tex]A=3x+7[/tex][tex]B=2x^2-1[/tex][tex]C=7x^2-3x[/tex]• You need to add them in order to find:
[tex]A+B+C[/tex]Set p that:
[tex]A+B+C=(3x+7)+(2x^2-1)+(7x^2-3x)[/tex]Remember the Sign Rules for Multiplication:
[tex]\begin{gathered} +\cdot+=+ \\ -\cdot-=+ \\ +\cdot-=- \\ -\cdot+=- \end{gathered}[/tex]Then, you know that the positive signs between the parentheses do not change the signs inside of them:
[tex]A+B+C=3x+7+2x^2-1+7x^2-3x[/tex]Combine the like terms (these are defined as those terms that have the same variables with the same exponents). Then:
[tex]A+B+C=9x^2+6[/tex]• Subtract the equations in order to find:
[tex]A-B-C[/tex]Set up that:
[tex]A-B-C=(3x+7)-(2x^2-1)-(7x^2-3x)[/tex]Simplify it by distributing the negative signs and then combining the like terms:
[tex]A-B-C=3x+7-2x^2+1-7x^2+3x[/tex][tex]A-B-C=-9x^2+6x+8[/tex]Hence, the answer is:
[tex]A+B+C=9x^2+6[/tex][tex]A-B-C=-9x^2+6x+8[/tex]