Factor the following: (x+4)(x+5)
Understand the Problem
The question is asking to identify the correct expansion of the factored expression (x+4)(x+5) from the given options. The expansion involves multiplying the two binomials and simplifying the resulting expression.
Answer
$x^2 + 9x + 20$
Answer for screen readers
$x^2 + 9x + 20$
Steps to Solve
- Apply the distributive property (also known as the FOIL method)
To expand the expression $(x+4)(x+5)$, we multiply each term in the first binomial by each term in the second binomial: $$(x+4)(x+5) = x(x+5) + 4(x+5)$$
- Distribute $x$ and $4$
Distribute $x$ to $(x+5)$ and $4$ to $(x+5)$: $$x(x+5) + 4(x+5) = x^2 + 5x + 4x + 20$$
- Combine like terms
Combine the $5x$ and $4x$ terms: $$x^2 + 5x + 4x + 20 = x^2 + 9x + 20$$
$x^2 + 9x + 20$
More Information
The expansion of $(x+4)(x+5)$ is $x^2 + 9x + 20$. This is a quadratic expression.
Tips
A common mistake is incorrectly applying the distributive property or making errors when combining like terms. For example, forgetting to multiply each term in the second binomial by each term in the first binomial, or incorrectly adding the coefficients of the $x$ terms. Careful attention to detail and practice can help avoid these mistakes.
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