Subtract $-4x^2 - x + 10$ from $x^2 + 10x$.
Understand the Problem
The question asks to subtract the polynomial $-4x^2 - x + 10$ from the polynomial $x^2 + 10x$. This involves distributing the negative sign to all terms in the second polynomial, then combining like terms.
Answer
$5x^2 + 11x - 10$
Answer for screen readers
$5x^2 + 11x - 10$
Steps to Solve
- Write out the subtraction
Write the expression for subtracting the second polynomial from the first: $(x^2 + 10x) - (-4x^2 - x + 10)$
- Distribute the negative sign
Distribute the negative sign to each term inside the second parenthesis: $x^2 + 10x + 4x^2 + x - 10$
- Combine like terms
Combine the $x^2$ terms, the $x$ terms, and the constant terms: $(x^2 + 4x^2) + (10x + x) - 10 = 5x^2 + 11x - 10$
$5x^2 + 11x - 10$
More Information
Polynomial subtraction involves distributing a negative sign, and then collecting like terms. This is similar to adding polynomials, but with careful attention to signs.
Tips
A common mistake is not distributing the negative sign to all terms in the polynomial being subtracted. For example, forgetting to change the sign of the constant term. Also, errors can happen during combining like terms, so it's important to double-check the coefficients.
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