To simplify the expression [tex]\(7 x^2 - 4 x + 4 x^2\)[/tex], follow these steps:
1. Combine like terms:
First, identify the like terms in the expression. In this case, [tex]\(7 x^2\)[/tex] and [tex]\(4 x^2\)[/tex] are like terms because they both have the same variable raised to the same power.
2. Add the coefficients of the like terms:
Combine the coefficients of [tex]\(x^2\)[/tex] terms:
[tex]\[
7 x^2 + 4 x^2 = (7 + 4) x^2 = 11 x^2
\][/tex]
3. Rewrite the expression:
After combining like terms, rewrite the expression. The term [tex]\(-4x\)[/tex] remains unchanged since it does not have any like terms:
[tex]\[
11 x^2 - 4 x
\][/tex]
4. Factor the expression (if possible):
Look for a common factor in the simplified expression. In this case, both terms contain [tex]\(x\)[/tex] as a factor:
[tex]\[
11 x^2 - 4 x = x (11 x - 4)
\][/tex]
Thus, the simplified expression is:
[tex]\[
x (11 x - 4)
\][/tex]
And that is the fully simplified form of the given expression [tex]\(7 x^2 - 4 x + 4 x^2\)[/tex].
