Question

How will you multiply\[{(2x - 6y)^2}\]?
\[
  A) 3{x^2} - 24xy + 26{y^2} \\
  B) 4{x^2} - 28xy + 36{y^2} \\
  C) 4{x^2} - 24xy + 36{y^2} \\
  D) 3{x^2} - 14xy + 36{y^2} \\
 \]

Answer 1

Hint: We will firstly expand the square and consider that in order to multiply the given two terms we need to multiply each individual term provided in the left parenthesis with the individual term provided in the right parenthesis. Here we will consider \[(2x - 6y)\] and \[(2x - 6y)\] as two separate binomials and by distributive method we will calculate the product.

Complete step by step solution:
Firstly we will expand the square so it becomes
\[(2x - 6y)(2x - 6y)\]
Now we will multiply each individual term by each individual term in the right parenthesis and through the use of distributive law of multiplication over addition twice we may find the product
So \[(2x - 6y)(2x - 6y)\]becomes
\[
   \Rightarrow 2x(2x - 6y) - 6y(2x - 6y) \\
   \Rightarrow 4{x^2} - 12xy - 6y(2x - 6y) \\
   \Rightarrow 4{x^2} - 12xy - 12xy + 36{y^2} \\
 \]
Later on we will combine like terms
\[4{x^2} - 24xy + 36{y^2}\]

Since the answer comes out to be \[4{x^2} - 24xy + 36{y^2}\] which means option \[C\] is correct.

Additional Information: Expanding the square makes it easier to solve. When we multiply two binomials, four multiplications take place. The order of these multiplications can take place in any order in which each of the first two terms is multiplied each of the second two terms.

Notes: We can also solve the above equation by column distributive setup also which is also known as vertical distributive set up. The method used to solve the equation is known as FOIL method which is a technique to distribute two binomials. Here, First stands for multiplying the term occurring in each binomial, Outer means multiplying the outermost term in the product while Inner term stands for multiplying the innermost terms and Last stands for multiplying the term occurring lastly in each binomial.