Simplify the given expression. $(5x+3y)^2 - (5x-3y)^2$
60xy
Let's simplify the expression: (5x+3y)^2 - (5x-3y)^2
This expression is in the form of a difference of squares:
(a^2 - b^2) = (a - b)(a + b)Here, let a = (5x + 3y) and b = (5x - 3y).
This means the expression can be written as:
((5x + 3y) - (5x - 3y))((5x + 3y) + (5x - 3y))Simplify inside the brackets:
- The first bracket: (5x + 3y) - (5x - 3y) = 5x + 3y - 5x + 3y = 6y
- The second bracket: (5x + 3y) + (5x - 3y) = 5x + 3y + 5x - 3y = 10x
Now, the expression simplifies to:
(6y)(10x) = 60xyThe correct answer is therefore: 60xy.
This simplification confirms the correct option is 60xy. The other options are incorrect calculations of the difference of squares.
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