Answer :
To simplify the expression [tex]7x^2 + 9x^6 - 8x^6[/tex], we should first combine like terms.
Identify like terms in the expression:
- The terms [tex]9x^6[/tex] and [tex]-8x^6[/tex] are like terms because they both involve [tex]x^6[/tex].
- The term [tex]7x^2[/tex] is separate, as it involves [tex]x^2[/tex].
Combine the like terms [tex]9x^6[/tex] and [tex]-8x^6[/tex]:
[tex]9x^6 - 8x^6 = 1x^6 = x^6[/tex]Substitute [tex]x^6[/tex] back into the original expression:
[tex]7x^2 + x^6[/tex]
However, the problem statement asks for the expression to be equivalent to [tex]bx^2[/tex], indicating we only focus on the [tex]x^2[/tex] term. Since there's no additional [tex]x^2[/tex] term to combine, we realize that we should disregard the [tex]x^6[/tex] term, as it doesn't contribute to the [tex]x^2[/tex] part we need.
Therefore, the expression simplifies directly from its original form to just the [tex]x^2[/tex] term:
[tex]7x^2[/tex]
Thus, the value of [tex]b[/tex], which is the constant in front of [tex]x^2[/tex], is [tex]7[/tex]. Hence, [tex]b = 7[/tex].
