(2x2+6x+1)+(3x2+3x+9)= 5x4+9x2+10

Question

True or false

Answer 1

To determine whether the equation $(2x^2+6x+1)+(3x^2+3x+9)=5x^4+9x^2+10$ is true or false, we can start by simplifying the left-hand side.

1. Combine like terms on the left-hand side:

$$(2x^2+6x+1)+(3x^2+3x+9)=(2x^2+3x^2)+(6x+3x)+(1+9)$$

2. This simplifies to:

$$5x^2+9x+10$$

Now we compare that to the right-hand side of the equation, $5x^4+9x^2+10$.

3. The left-hand side is $5x^2+9x+10$ and the right-hand side is $5x^4+9x^2+10$.

Clearly, the left-hand side does not equal the right-hand side because:

• The left-hand side contains no $x^4$ term and has a linear term $9x$.
• The right-hand side has a $5x^4$ term, $9x^2$ term, and no linear term.

Therefore, the equation is false.