Expanding and simplifying an expression involves multiplying out and combining like terms to create a simpler, equivalent expression. This can help make the expression easier to work with and understand.
To expand and simplify an expression, you need to use the distributive property and FOIL method. This involves multiplying each term in the first set of parentheses by each term in the second set of parentheses, and then combining like terms.
The steps for expanding and simplifying (3x-5)^2 are:1. Square the first term: (3x)^2 = 9x^22. Multiply the first and second terms by 2: 2(3x)(-5) = -30x3. Square the second term: (-5)^2 = 254. Combine the terms: 9x^2 - 30x + 25
When expanding and simplifying, you can use the negative sign to distribute or combine terms. For example, (-3x)^2 = (-3x)(-3x) = 9x^2. And (-3x+5)(2x-4) = -6x^2 + 22x - 20.
It is important to check your work when expanding and simplifying because it is easy to make mistakes when dealing with multiple terms and operations. Checking your work can help catch any errors and ensure that the final expression is correct.