Simplify the expression. (2h - 1)(h + 6) + (h + 9)
Understand the Problem
The question asks to simplify the given algebraic expression, which involves expanding and combining like terms.
Answer
The simplified expression is $2h^2 + 12h + 3$.
Answer for screen readers
The simplified expression is:
$$ 2h^2 + 12h + 3 $$
Steps to Solve
- Expand the first expression
Start by using the distributive property (also known as the FOIL method for binomials) on the first part, $(2h - 1)(h + 6)$.
$$ (2h - 1)(h + 6) = 2h \cdot h + 2h \cdot 6 - 1 \cdot h - 1 \cdot 6 $$
This simplifies to:
$$ 2h^2 + 12h - h - 6 = 2h^2 + 11h - 6 $$
- Combine with the second expression
Now combine this result with the second expression, $(h + 9)$:
$$ 2h^2 + 11h - 6 + (h + 9) $$
- Combine like terms
Now combine the like terms:
$$ 2h^2 + (11h + h) + (-6 + 9) $$
This simplifies to:
$$ 2h^2 + 12h + 3 $$
The simplified expression is:
$$ 2h^2 + 12h + 3 $$
More Information
This is the final simplified expression resulting from expanding and combining like terms in the original polynomial. Polynomial simplification often involves careful application of distribution and combination of like terms.
Tips
- Neglecting to distribute correctly: Make sure to distribute each term in the first factor to each term in the second factor.
- Forgetting to combine like terms: Always combine all like terms after simplifying each part of the expression.
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