In Exercises 85–96, simplify each algebraic expression. 5(3y−2)−(7y+2)

Guida verificata passo dopo passo

Distribute the 5 across the terms inside the parentheses (3y−2). This means multiplying 5 by each term: 5 * 3y and 5 * -2.

Simplify the distribution: 5 * 3y becomes 15y, and 5 * -2 becomes -10. So the expression now looks like 15y - 10 - (7y + 2).

Distribute the negative sign across the terms inside the parentheses (7y+2). This means multiplying -1 by each term: -1 * 7y and -1 * 2.

Simplify the distribution: -1 * 7y becomes -7y, and -1 * 2 becomes -2. So the expression now looks like 15y - 10 - 7y - 2.

Combine like terms: Add the terms with 'y' (15y and -7y) and combine the constants (-10 and -2). This will give you the simplified expression.

Risposta video verificata per un problema simile:

Questa soluzione video è stata consigliata dai nostri tutor come utile per risolvere questo problema.

Durata del video:

Concetti chiave

Ecco i concetti essenziali che devi comprendere per rispondere correttamente alla domanda.

Distributive Property

The Distributive Property states that a(b + c) = ab + ac. This property allows us to multiply a single term by each term within a set of parentheses. In the given expression, applying the distributive property to 5(3y - 2) means multiplying 5 by both 3y and -2, which simplifies the expression.

Video consigliato:

04:15

Multiply Polynomials Using the Distributive Property

Combining Like Terms

Combining like terms involves adding or subtracting terms that have the same variable raised to the same power. In the expression, after distributing, you will have terms involving 'y' and constant terms. Grouping these similar terms together allows for simplification, leading to a more concise expression.

Video consigliato:

5:22

Combinations

Negative Sign Distribution

When a negative sign is in front of parentheses, it affects all terms inside the parentheses. For example, -(7y + 2) becomes -7y - 2 when distributed. Understanding how to properly distribute the negative sign is crucial for accurately simplifying the expression and avoiding errors in the final result.

Video consigliato:

04:15

Multiply Polynomials Using the Distributive Property

Pratica correlata

Domanda del libro di testo

Perform the indicated computations. Write the answers in scientific notation. If necessary, round the decimal factor in your scientific notation answer to two decimal places. $(6.1 \times 10^{- 8}) (2 \times 10^{- 4})$