Question

Multiply and combine like terms(x+3)^2+(x+4)^2-3(x^2-3)

Answer 1

Step-by-step explanation:

First we have to solve the squared binomials:

`(a\pm b)^2=a^2\pm2ab+b^2`

(x+3)²:

`\begin{gathered} (x+3)^2=x^2+2\cdot3x+3^2 \\ (x+3)^2=x^2+6x+9 \end{gathered}`

(x+4)²:

`\begin{gathered} (x+4)^2=x^2+2\cdot4\cdot x+4^2 \\ (x+4)^2=x^2+8x+16 \end{gathered}`

Now we have:

`\begin{gathered} (x+3)^2+(x+4)^2-3(x^2-3) \\ (x^2+6x+9)+(x^2+8x+16)-3(x^2-3) \end{gathered}`

We have to distribute -3 into the last term:

`x^2+6x+9+x^2+8x+16-3x^2+9`

Now we have to add like terms:

`(x^2+x^2-3x^2)+(6x+8x)+(9+16+9)=-x^2+14x+34`

Answer:

(x+3)²+(x+4)²-3(x²-3) = -x² + 14x + 34