Fully factorise 14h² + 63h
Understand the Problem
The question is asking to fully factor the expression 14h² + 63h. The approach involves identifying common factors in the expression and rewriting it in its factored form.
Answer
$7h(2h + 9)$
Answer for screen readers
The fully factored form of the expression is $7h(2h + 9)$.
Steps to Solve
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Identify the common factor Examine the coefficients and variables in the expression $14h^2 + 63h$. The coefficients are 14 and 63, and both terms contain the variable $h$.
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Find the greatest common factor (GCF) The GCF of the coefficients 14 and 63 can be calculated:
- Factors of 14: 1, 2, 7, 14
- Factors of 63: 1, 3, 7, 9, 21, 63
The GCF is 7. The common variable factor is $h$. Thus, the overall GCF is $7h$.
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Factor out the GCF Rewrite the expression by factoring out the GCF: $$ 14h^2 + 63h = 7h(2h + 9) $$
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Write the fully factored form Now, the expression is fully factored as: $$ 14h^2 + 63h = 7h(2h + 9) $$
The fully factored form of the expression is $7h(2h + 9)$.
More Information
Factoring helps simplify expressions and can be useful in solving equations. The GCF method is a foundational technique in algebra that prepares students for more complex factoring, such as factoring trinomials and recognizing quadratic forms.
Tips
Common mistakes include:
- Not identifying the GCF correctly. Always list factors carefully.
- Forgetting to include all parts of the GCF (like variables) when factoring out. Ensure to factor out both coefficients and variables together.
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