Expand and simplify this expression: −5𝑥(5𝑥−5𝑦)−5x(5x−5y)
Question
Expand and simplify this expression: −5𝑥(5𝑥−5𝑦)−5x(5x−5y)
Solution 1
First, distribute the -5x across each term in the first parenthesis:
-5x * 5x = -25x^2 -5x * -5y = 25xy
So, -5x(5x-5y) simplifies to -25x^2 + 25xy.
Next, distribute the -5x across each term in the second parenthesis:
-5x * 5x = -25x^2 -5x * -5y = 25xy
So, -5x(5x-5y) simplifies to -25x^2 + 25xy.
Finally, add the two simplified expressions together:
(-25x^2 + 25xy) + (-25x^2 + 25xy) = -50x^2 + 50xy
So, the expression -5x(5x-5y) - 5x(5x-5y) expands and simplifies to -50x^2 + 50xy.
Solution 2
First, distribute -5x across the terms in the parentheses:
-5x * 5x = -25x^2 -5x * -5y = 25xy
So, -5x(5x-5y) simplifies to -25x^2 + 25xy.
Now, do the same for the second part of the expression:
-5x * 5x = -25x^2 -5x * -5y = 25xy
So, -5x(5x-5y) simplifies to -25x^2 + 25xy.
Finally, add the two simplified expressions together:
(-25x^2 + 25xy) + (-25x^2 + 25xy) = -50x^2 + 50xy
So, the expression -5x(5x-5y) - 5x(5x-5y) expands and simplifies to -50x^2 + 50xy.
Solution 3
First, distribute -5x across the terms in the parentheses:
-5x * 5x = -25x^2 -5x * -5y = 25xy
So, -5x(5x-5y) simplifies to -25x^2 + 25xy.
Now, do the same for the second part of the expression:
-5x * 5x = -25x^2 -5x * -5y = 25xy
So, -5x(5x-5y) simplifies to -25x^2 + 25xy.
Finally, add the two simplified expressions together:
(-25x^2 + 25xy) + (-25x^2 + 25xy) = -50x^2 + 50xy
So, the expression -5x(5x-5y) - 5x(5x-5y) expands and simplifies to -50x^2 + 50xy.
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