To simplify the expression [tex]\( 3a^2 + 14a^2 \)[/tex] using the distributive property, we proceed as follows:
1. Identify the coefficients of the like terms:
- The first term is [tex]\( 3a^2 \)[/tex], where the coefficient is [tex]\( 3 \)[/tex].
- The second term is [tex]\( 14a^2 \)[/tex], where the coefficient is [tex]\( 14 \)[/tex].
2. Add the coefficients of the like terms:
- The sum of the coefficients is [tex]\( 3 + 14 \)[/tex].
3. Calculate the result of the addition:
- [tex]\( 3 + 14 = 17 \)[/tex].
4. Write the simplified expression with the combined coefficients:
- The combined coefficient [tex]\( 17 \)[/tex] is paired with [tex]\( a^2 \)[/tex].
Thus, the simplified expression is [tex]\( 17a^2 \)[/tex].
So, the step-by-step solution is:
[tex]$
3 a^2+14 a^2=(3+[14]) a^2=[17] a^2
$[/tex]
Therefore, the simplified expression is [tex]\( 17a^2 \)[/tex].
