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.

(4xy² − xy)²

Accepted Answer

Hello, everyone. We are gonna perform multiplication on the given expression. Open parentheses, two CD cubed minus CD, closed parentheses squared. Our answer choices are a four C squared D raised to the sixth power minus four C raised to the fourth power D squared plus C squared D squared B four C squared D raised the sixth power minus four C raised to the fourth power D raise to the fourth power plus C squared D squared C four C squared D raised to the sixth power minus four C squared D raised to the fourth power plus C squared D squared D four C squared D raised to the sixth power minus eight C squared D raised to the fourth power plus C squared D squared. Going back to our original expression, we have open parentheses, two CD cubed minus CD, closed parentheses. Quan D squared. I recall that when I have a binomial squared, there's a shortcut I can use. If you don't recall the shortcut, you absolutely could write this as two CD cubed minus CD multiplied by the parentheses, two CD cubed minus CD and use foil. However, there is a shorter way when you have a binomial squared, you have few steps. So when you have a binomial square, we're gonna end up with a trinomial. So our first term in our trinomial will be the first term from the binomial squared. So it's the first term of the binomial squared. So in this case, that would be 2 CD Cubed and that whole thing will be squared. The second term in our trinomial comes from multiplying the two terms of the binomial together and then multiplying it by two. So it's the product of the two terms in the Bino meal and then times two or multiplied by two. So in this case, this would be, and I'm gonna put it in parentheses, two CD cubed multiplied by negative CD multiplied by two. And then our third term is the second term in the binomial squared. So we have in this case CD squared. So now that I've set it up, I'm gonna do the multiplication. And when you get more comfortable with this, this flows a lot faster. So squaring the entire term, two CD raised to the third power squared. So two squared is four C squared is C squared D cubed squared. I recall that when I raise a power to a power I multiply my exponents. So that will be D raised to the sixth power. My middle term, I'm gonna start by multiplying the constants. So two times two is four C times C is C squared, D cubed multiplied by D. When we have like bases multiplied, we add our exponents. So we get d raised to the fourth power. And actually, there's a negative in there. So that whole thing times negative one will make this a negative for C squared D rays to the fourth power and then CD squared. So plus C squared D squared. So our trinomial as our answer is four C squared D raise the sixth power minus four C squared D raise to the fourth power plus C squared D squared. And this is answer choice C have a nice day.

In Exercises 55–68, multiply using one of the rules for the square of a binomial. (4xy² − xy)²

Key Concepts

Binomial

Square of a Binomial

Polynomial Expansion

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