Question

Simplify

1. y2 + 3y^2
2. 4x + 15 - 3x +10
3. -10x + 2x + 8x

Answer 1

1) Both y^2 and 3y^2 have the same base so you can combine the terms to make 4y^2, but if you were to have y^2 and y^3, you wouldn’t be able to combine the terms and make y^5 because they are raised to different powers!

2) You can simplify the expression by combining terms. It’s best in this situation to bring terms of the same base or same layout next to each other so you don’t make a mistake, rewrite as 4x-3x+15+10. So you then simplify and it becomes x+25.

3) Similar to the last one, this one only needs to be simplified as they are all ‘n’ amount of x. And if it helps, ignore the x’s and just do normal arithmetic maths then include the x in your answer or at the end of your working, so -10+2+8. But since 2+8=10, -10+10=0 so your answer would be 0x or just 0!

Hope this helps!

Answer 2

Explanation:

1. To simplify the expression y^2 + 3y^2, we can combine the like terms. Since both terms have the same base, which is y, we can add the exponents together. This gives us 4y^2.

2. In the expression 4x + 15 - 3x + 10, we can simplify it by combining the like terms. The like terms here are the x terms (4x and -3x) and the constant terms (15 and 10). When we combine the x terms, we subtract the coefficients: 4x - 3x = 1x = x. For the constant terms, we simply add them together: 15 + 10 = 25. Therefore, the simplified expression is x + 25.

3. In the expression -10x + 2x + 8x, we can combine the like terms, which are the x terms. When we add or subtract terms with the same base, we keep the base and add or subtract the coefficients. In this case, we have -10x, 2x, and 8x. Adding them together, we get -10x + 2x + 8x = -10x + (2x + 8x) = -10x + 10x = 0. Therefore, the simplified expression is 0.

Remember, when simplifying expressions, it's important to combine like terms and perform any necessary operations according to the rules of algebra. This helps us to simplify complex expressions and make them easier to work with.