Questions: Simplify. (7 u^2+3)-(2 u^2-6 u+4)

Transcript text: Simplify. \[ \left(7 u^{2}+3\right)-\left(2 u^{2}-6 u+4\right) \]

Solution

Solution Steps

To simplify the given expression, we need to distribute the negative sign through the second set of parentheses and then combine like terms.

Step 1: Distribute the Negative Sign

We start with the expression: \[ (7u^{2} + 3) - (2u^{2} - 6u + 4) \] Distributing the negative sign through the second set of parentheses gives us: \[ 7u^{2} + 3 - 2u^{2} + 6u - 4 \]

Step 2: Combine Like Terms

Next, we combine the like terms:

For \(u^{2}\) terms: \(7u^{2} - 2u^{2} = 5u^{2}\)
For \(u\) terms: \(6u\) (there are no other \(u\) terms to combine with)
For constant terms: \(3 - 4 = -1\)

Thus, the expression simplifies to: \[ 5u^{2} + 6u - 1 \]

Final Answer

The simplified expression is \[ \boxed{5u^{2} + 6u - 1} \]

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