¿Cuál es el resultado de efectuar (5x + 7)(2x - 3)?
Understand the Problem
La pregunta es una expresión algebraica y nos pide simplificarla. Esto implica expandir el producto de los dos binomios y luego combinar los términos semejantes para obtener la forma simplificada.
Answer
$10x^2 - x - 21$
Answer for screen readers
$10x^2 - x - 21$
Steps to Solve
- Expanding the product
We will use the distributive property (also known as FOIL) to expand the product of the two binomials $(5x + 7)(2x - 3)$.
$(5x + 7)(2x - 3) = 5x(2x) + 5x(-3) + 7(2x) + 7(-3)$
- Simplifying each term
Now, perform each multiplication:
$5x(2x) = 10x^2$ $5x(-3) = -15x$ $7(2x) = 14x$ $7(-3) = -21$
- Combining the terms
Substitute these results back into the expression:
$10x^2 - 15x + 14x - 21$
- Combining like terms
Combine the $x$ terms:
$-15x + 14x = -x$
- Final simplified expression
So the simplified expression is:
$10x^2 - x - 21$
$10x^2 - x - 21$
More Information
The result of expanding and simplifying $(5x + 7)(2x - 3)$ is $10x^2 - x - 21$.
Tips
A common mistake is distributing the terms incorrectly, especially with the negative sign in the second binomial. Another mistake could be incorrectly multiplying the coefficients or the variables.
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