Factor 10a^2b^2 - 13ab^3 - 3b.
Understand the Problem
The question requires us to factor the given expression: 10a^2b^2 - 13ab^3 - 3b. Factoring involves breaking down the expression into simpler terms that, when multiplied together, give the original expression.
Answer
$b(10a^2b - 13ab^2 - 3)$
Answer for screen readers
$b(10a^2b - 13ab^2 - 3)$
Steps to Solve
- Identify the common factor
Observe that each term in the expression $10a^2b^2 - 13ab^3 - 3b$ has 'b' as a common factor.
- Factor out the common factor
Factor out 'b' from the expression:
$10a^2b^2 - 13ab^3 - 3b = b(10a^2b - 13ab^2 - 3)$
- Check for further factorization within the parentheses
Let's examine the expression within the parenthesis, $10a^2b - 13ab^2 - 3$. There are no apparent common factors among all three terms inside the parenthesis, and it doesn't seem to fit any standard factoring patterns directly. However, let's re-examine if we made a mistake factoring out the $b$, we did not. The expression within the parentheses cannot be factored further using simple methods.
- Write the final factored form
Since the expression inside the parentheses cannot be factored further, the factored form of the original expression is:
$b(10a^2b - 13ab^2 - 3)$
$b(10a^2b - 13ab^2 - 3)$
More Information
Factoring is the reverse process of expansion. We look for common elements or patterns that can simplify the expression into a product of terms.
Tips
A common mistake is to stop after factoring out 'b' and not checking if the expression inside the parentheses can be factored further. Another mistake would be trying to force a factoring pattern that doesn't actually fit the expression.
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