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.
- Combine like terms on the left-hand side:
\[ (2x^2 + 6x + 1) + (3x^2 + 3x + 9) = (2x^2 + 3x^2) + (6x + 3x) + (1 + 9) \]
- This simplifies to:
\[ 5x^2 + 9x + 10 \]
Now we compare that to the right-hand side of the equation, \(5x^4 + 9x^2 + 10\).
- 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.
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