Questions: (8x^6-8x^4+12)-(4x^6+13x^4-8)

Transcript text: $\left(8 x^{6}-8 x^{4}+12\right)-\left(4 x^{6}+13 x^{4}-8\right)$

Solution

Solution Steps

Step 1: Distribute the Negative Sign

We start with the expression: \[ (8 x^{6} - 8 x^{4} + 12) - (4 x^{6} + 13 x^{4} - 8) \] Distributing the negative sign through the second set of parentheses gives us: \[ 8 x^{6} - 8 x^{4} + 12 - 4 x^{6} - 13 x^{4} + 8 \]

Step 2: Combine Like Terms

Next, we combine the like terms. For the $ x^{6} $ terms: \[ 8 x^{6} - 4 x^{6} = 4 x^{6} \] For the $ x^{4} $ terms: \[ -8 x^{4} - 13 x^{4} = -21 x^{4} \] And for the constant terms: \[ 12 + 8 = 20 \]

Step 3: Write the Simplified Expression

Putting it all together, we obtain the simplified expression: \[ 4 x^{6} - 21 x^{4} + 20 \]