How do you multiply (x−2y)2?

2 Answers
smendyka
Mar 3, 2018

See a solution process below:

Explanation:

This is a special form of the quadratic:

(a−b)2=(a−b)(a−b)=a2−2xb+b2

Let:

  • a=x

  • b=2y

Substituting gives:

(x−2y)2⇒

(x−2y)(x−2y)⇒

x2−(2×x×2y)+(2y)2⇒

x2−4xy+4y2

Jacobi J.
Mar 3, 2018

x2−4xy+4y2

Explanation:

We can rewrite (x−2y)2 as (x−2y)(x−2y). The expression I have in blue, we can use FOIL to multiply.

(x−2y)(x−2y)

FOIL tells us that we multiply the first terms, outside terms, inside terms and last terms respectively. We get:

  • Firsts (x⋅x)=x2
  • Outsides (x⋅−2y)=−2xy
  • Insides (−2y⋅x)=−2xy
  • Lasts (−2y⋅−2y)=4y2

NOTE:Whenever we're multiplying binomials, we can use FOIL

Our new expression is as follows:

x2−2xy−2xy+4y2

We can combine like terms to get:

x2−4xy+4y2

Alternatively, we could have separated (x−2y)(x−2y) into two expressions if you're not a FOIL person. This is the same as doing:

x(x−2y)−2y(x−2y)

We can distribute the x and the −2y respectively to get:

x2−2xy−2xy+4y2

And we could combine like terms to get:

x2−4xy+4y2

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