Simplify x * 7x^4
Understand the Problem
The question is asking to simplify the given expression by performing multiplication and combining like terms.
Answer
$-x^2 + 4x - 15$
Answer for screen readers
$-x^2 + 4x - 15$
Steps to Solve
- Expand the first term $(x-3)(x+5)$ using the distributive property (FOIL method)
$(x-3)(x+5) = x(x) + x(5) -3(x) -3(5) = x^2 + 5x - 3x - 15 = x^2 + 2x - 15$
- Expand the second term $2x(x-1)$ using the distributive property
$2x(x-1) = 2x(x) - 2x(1) = 2x^2 - 2x$
- Substitute the expanded forms back into the original expression
$(x-3)(x+5) - 2x(x-1) = (x^2 + 2x - 15) - (2x^2 - 2x)$
- Distribute the negative sign in front of the second term
$(x^2 + 2x - 15) - (2x^2 - 2x) = x^2 + 2x - 15 - 2x^2 + 2x$
- Combine like terms
$x^2 - 2x^2 + 2x + 2x - 15 = -x^2 + 4x - 15$
$-x^2 + 4x - 15$
More Information
The simplified form of the expression $(x-3)(x+5) - 2x(x-1)$ is $-x^2 + 4x - 15$.
Tips
A common mistake is not distributing the negative sign correctly when subtracting the second term. Remember to change the sign of each term inside the parentheses when subtracting. Another common mistake is combining unlike terms. Make sure to only combine terms with the same variable and exponent.
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