# What is #(6x^2+3x)+(2x^2+6x)#?

##### 3 Answers

#8x^2+9x#

#### Explanation:

Given -

#(6x^2+3x)+(2x^2+6x)#

#6x^2+3x+2x^2+6x#

#8x^2+9x#

Remove the parentheses and add the x^2 terms together. You get 6x^2 + 2 x^2 = 8 x^2.

Then do the same with the x terms

3x + 6x = 9x

8 x^2 + 9x

In summary

8 x^2 + 9x

#### Explanation:

Here is a method of solution demonstrating some fundamental properites of arithmetic:

Addition is associative:

#a+(b+c) = (a+b)+c#

Addition is commutative:

#a+b = b+a#

Multiplication is left and right distributive over addition:

#a(b+c) = ab+ac#

#(a+b)c = ac+bc#

Hence we find:

#(6x^2+3x)+(2x^2+6x)#

#=6x^2+(3x+(2x^2+6x))" "# (by associativity)

#=6x^2+((2x^2+6x)+3x)" "# (by commutativity)

#=6x^2+(2x^2+(6x+3x))" "# (by associativity)

#=(6x^2+2x^2)+(6x+3x)" "# (by associativity)

#=(6+2)x^2+(6+3)x" "# (by right distributivity twice)

#=8x^2+9x#