Expand (3x-y)²: Converting to Addition and Multiplication Forms

Video Solution

Solution Steps

00:00 Express the expression as a sum and product

00:07 A factor times itself is actually squared

00:13 Break down the power into multiplication by itself

00:27 Use the shortened multiplication formulas to expand the brackets

00:44 Calculate the squares and products

00:57 And this is the solution to the question

Step-by-Step Solution

To solve this problem, let's start by identifying the parts of the binomial:

The expression $(3x-y)^2$ represents a binomial squared.
We recognize it has the form $(a-b)^2$ where $a = 3x$ and $b = y$ .
Using the formula for the square of a difference: $(a-b)^2 = a^2 - 2ab + b^2$ , we find the expanded form.

Let's apply the formula:

Step 1: Expand $(3x-y)^2$ using the formula:
$(3x-y)^2 = (3x)^2 - 2(3x)(y) + y^2$

Step 2: Calculate each part:
$(3x)^2 = 9x^2$
$-2(3x)(y) = -6xy$
$y^2$ stays as $y^2$

Step 3: Combine these results to get the addition form:
$9x^2 - 6xy + y^2$

The expression in multiplication form, as provided, is just repeating the factors:
$(3x-y)(3x-y)$

Therefore, the expression rewritten as addition is $9x^2 - 6xy + y^2$ and as multiplication $(3x-y)(3x-y)$ .