Question

How do you combine like terms for $3x^2+21x+5x+10x^2$?

Answer 1

Combine the like terms in $3x^2+21x+5x+10x^2$.

The terms in a polynomial that become equal if their numerical coefficient and signs are removed are known as like terms. For example, in the given polynomial $3x^2+21x+5x+10x^2$, $3x^2$ and $10x^2$ are like terms because they both become $x^2$ if their coefficients are removed. Like terms are first grouped together and then their common factors are taken out. The numerical expression in the brackets is then simplified to obtain the combined result.

This process is shown below for the given polynomial $3x^2+21x+5x+10x^2$:

$\begin{array}{rcl}3x^2+21x+5x+10x^2& =& 3x^2+10x^2+21x+5x\\ & =& x^2\left(3+10\right)+x\left(21+5\right)\\ & =& x^2\times 13+x\times 26\\ & =& 13x^2+26x\end{array}$

Hence, the like terms of $3x^2+21x+5x+10x^2$ can be combined to get $\mathbf{13}{\mathit{x}}^{\mathbf{2}}\mathbf{+}\mathbf{26}\mathit{x}$.