Question

Use a vertical format or a horizontal format to add or subtract. $$\left(6.2 b^{4}-3.1 b+8.5\right)+\left(-4.7+5.8 b^{2}-2.4 b^{4}\right)$$

Short answer

The simplified algebraic expression after the addition operation is \(3.8 b^{4} + 5.8 b^{2} - 3.1b + 3.8\)

Step-by-step solution

Grouping terms

Rewrite the expression by grouping the similar terms together. The similar terms are the ones with the same exponent of \( b \). This gives: \(6.2 b^{4}-2.4 b^{4}+5.8 b^{2}-3.1b-4.7+8.5\)

Simplification of terms

Add or subtract the coefficients of like terms. The coefficients are the numbers before the \( b \) terms. This results in \( (6.2-2.4) b^{4} + 5.8 b^{2} - 3.1b + (-4.7+8.5)\).

Calculation

Perform the addition or subtraction of the coefficients to get the simplified expression. This yields \(3.8 b^{4} + 5.8 b^{2} - 3.1b + 3.8 \)