In Exercises 55–68, multiply using one of the rules for the squar...

Question

In Exercises 55–68, multiply using one of the rules for the square of a binomial.

(5x − 3y)²

Accepted Answer

Hello, everyone. We're gonna perform multiplication on the given expression. We have open parentheses. Seven A minus four B closed parentheses squared. Our answer choices are a 49 A squared plus 28 A B plus 16 B squared, B 49 A squared plus 56 A B plus 16 B squared C 49 A squared minus 28 A B plus 16 B squared D 49 A squared minus 56 A B plus B squared. So we have a binomial of seven A minus four B that's in parentheses and it's squared. So when we have a binomial squared, we could write it next to itself and foil it out or there's a pattern to these. The pattern is that when you have a binomial squared, you can get your trinomial by first squaring. The first term from the binomial. So seven A squared, seven squared is 49 A squared is A squared. For the last term in your trinomial, you square. The last term from the binomial. So square, the last term is four B squared. So four squared is 16 B squared is B squared. That will be A plus sign in front of it. And to find our middle term, you take the product of the two terms of the binomial and then we double it. So the product of the two terms from our binomial would be seven A multiplied by negative four B. So that'd be negative 28 A B doubled. So multiplied by two be negative 56 A B. So the shortcut to this, we squared, the first term, we squared the last term we took the product of the two terms in the binomial and then we doubled it to find our middle term. And that gave us the trinomial 49 A squared minus 56 A B plus 16 B squared, which is answer choice D have a nice day.

In Exercises 55–68, multiply using one of the rules for the square of a binomial. (5x − 3y)²

Key Concepts

Binomial

Square of a Binomial

Algebraic Expansion

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