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Multiply and simplify (5a + 2bc) (5a - 2bc)

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Banaszek168

⇒ (a + b)(a - b) = a² - b² Multiply and simplify : [latex](5a + 2bc) (5a - 2bc) \\ =25a^2+10abc-10abc-4bc^2 \\ =25a^2-4b^2c^2[/latex]

BettieZumbrunnen

One of the tools that's great to keep in your algebra toolbox for the rest of your life is: The product of (sum of 2 things) (difference of 2 things) = (difference in their squares). For example:  (x + y) (x - y) = (x² - y²) When you're trying to factor algebra expressions, it's always good to keep your eyes open for the difference of two squares, and remember that it's going to be (sum) x (difference) of the things that they're squares of. Here you have (a sum) x (a difference) of the same 2 things: (5a + 2bc) (5a - 2bc) You can multiply them out, or just use the little tool above: (5a)² = 25a² (2bc)² = 4b²c² So (their sum) x (their difference) is (25a² - 4b²c²) .

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