Find the sum of the following expression: (x+3)(2x+5)+7x+5
Understand the Problem
The question requires finding the sum of the expression (x+3)(2x+5)+7x+5. This involves expanding the product of the binomials (x+3) and (2x+5), and then combining like terms to simplify the entire expression.
Answer
$2x^2 + 18x + 20$
Answer for screen readers
$2x^2 + 18x + 20$
Steps to Solve
- Expand the product of the binomials (x+3) and (2x+5)
Use the distributive property (also known as FOIL) to multiply the two binomials: $$ (x+3)(2x+5) = x(2x) + x(5) + 3(2x) + 3(5) $$ $$ = 2x^2 + 5x + 6x + 15 $$
- Combine like terms from the expansion
Combine the $x$ terms: $$ 2x^2 + (5x + 6x) + 15 = 2x^2 + 11x + 15 $$
- Substitute the simplified expansion back into the original expression
Replace $(x+3)(2x+5)$ with $2x^2 + 11x + 15$ in the original expression: $$ (2x^2 + 11x + 15) + 7x + 5 $$
- Combine like terms in the entire expression
Combine the $x$ terms and the constant terms: $$ 2x^2 + (11x + 7x) + (15 + 5) = 2x^2 + 18x + 20 $$
$2x^2 + 18x + 20$
More Information
The simplified form of the given expression $(x+3)(2x+5)+7x+5$ is $2x^2 + 18x + 20$. This is a quadratic expression.
Tips
A common mistake is not correctly applying the distributive property when expanding the binomials. For example, forgetting to multiply each term in the first binomial by each term in the second binomial. Another error is combining unlike terms, such as adding an $x^2$ term to an $x$ term. To avoid these mistakes, write out each step clearly and double-check your work.
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