Question

5*​15^​(x)-​3*​5^​(x+​1)-​3^(​x)+​3

Answer 1

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Answer 2

To simplify the expression 515^x - 35^(x+1) - 3^x + 3, let's break it down step by step:

Step 1: Simplify the powers of 5 and 3.

• 15 can be written as 3 * 5.
• 5^(x+1) can be written as 5^x * 5.
• 3^x remains unchanged.

Step 2: Substitute the simplified forms into the expression.

515^x - 35^(x+1) - 3^x + 3 = 5 * (3 * 5)^x - 3 * (5^x * 5) - 3^x + 3

Step 3: Use the property (a * b)^c = a^c * b^c to further simplify.

= 5 * 3^x * 5^x - 3 * 5^x * 5 - 3^x + 3

Step 4: Group like terms and combine them.

= 5^x * 3^x - 15 * 5^x - 3^x + 3

Step 5: Factor out common terms.

= (5^x * 3^x - 3^x) - 15 * 5^x + 3

Step 6: Factor out 3^x from the first two terms.

= 3^x * (5^x - 1) - 15 * 5^x + 3

Now the expression is simplified as much as possible. If you have specific values for x, you can substitute them into the expression to get the final result. Otherwise, this is the simplified form of the expression.