Hiya. I have 7 expressions that I have been asked to simplify. I worked all of them out, and if you could, I'd like you to check my work for me.

Here they are:

1. (x^2 + 3x - 9) + (-4x^2 + 2x - 3)

My answer: -4x^4 + 5x - 12

2. (x - 2)(3x + 5)

My answer: 3x^2 - 30x - 10

3. (r + 3)^2

My answer: r^2 + 6r + 9

4. (p^2 + 4p - 23) - (3p^2 - 23p - 23)

My answer: 3p^4 - 19p - 46

5. (5z - 2)(5z + 2)

My answer: 25z^4 - 4

6. (2m - 4)(m^2 + 2m + 4)

My answer: 2m^3

7. (3x - 2)(2x - 3)

My answer: 6x^2 - 13x + 6

I know there were quite a few there, so I really appreciate you helping me out. If I made any mistakes, please let me know what I did wrong so I can correct it. Thank you so much!

1. (x^2 + 3x - 9) + (-4x^2 + 2x - 3)

My answer: -4x^4 + 5x - 12
-------------------------------
my answer, add like terms
x^2 - 4 x^2 = - 3 x^2 for example

-3 x^2 + 5 x -12

2. (x - 2)(3x + 5)

My answer: 3x^2 - 30x - 10
---------------------------
My answer, either FOIL or use distributive property
FOIL
3 x^2 + 5 x - 6 x -10
= 3 x^2 - x - 10
distributive property
x(3x+5) -2(3x+5)
3 x^2 + 5 x - 6 x - 10 remarkably similar

#1 should be

-3x^2 + 5x- 12

#2
3x^2+ 5x - 6x - 10 = 3x^2- x - 10

#3, good, yeahhh
#4, -2p^2 + 27p
#5, yeahhh
#6 good grief!!!
= 2m^3 + 4m^2 + 8m - 4m^2 - 8m - 16
= 2m^3 - 16

#7, correct

3. (r + 3)^2

My answer: r^2 + 6r + 9 YES

something like 6 use that distributive property

6. (2m - 4)(m^2 + 2m + 4)
2m (m^2 + 2m + 4) = 2 m^3 +4 m^2 + 8 m
-4 (m^2 + 2m + 4) = 0 m^3 -4 m^2 - 8 m -16
-----------------------------------add
2 m^3 -16

Thanks Damon and Reiny for your help!

Hi! I'd be happy to check your work and help you understand the process of simplifying each expression.

1. (x^2 + 3x - 9) + (-4x^2 + 2x - 3)

To simplify this expression, first combine like terms. Add the coefficients of the terms with the same variable and exponent. So, for the x^2 term, the coefficient would be 1 + (-4) = -3. For the x term, the coefficient would be 3 + 2 = 5. And for the constant term (no x), it would be -9 + (-3) = -12.

So the simplified expression is: -3x^2 + 5x - 12.

Your answer is incorrect. You mistakenly changed the sign of the x^2 term and didn't combine the coefficients of the like terms appropriately.

2. (x - 2)(3x + 5)

To simplify this expression, you can use the distributive property to multiply. Multiply each term of the first expression (x - 2) by each term of the second expression (3x + 5). Then combine like terms if any.

So, (x - 2)(3x + 5) can be expanded as:

x * (3x + 5) - 2 * (3x + 5)

= 3x^2 + 5x - 6x - 10

= 3x^2 - x - 10

Your answer is incorrect. You only distributed one term and made a mistake in combining the coefficients of the x terms.

3. (r + 3)^2

To simplify this expression, you can use the concept of the "square of a binomial." Taking the square of a binomial follows the formula:

(a + b)^2 = a^2 + 2ab + b^2

So, applying this formula to (r + 3)^2:

= r^2 + 2(r)(3) + 3^2

= r^2 + 6r + 9

Your answer is correct!

4. (p^2 + 4p - 23) - (3p^2 - 23p - 23)

To simplify this expression, you need to distribute the negative sign inside the second parentheses. Then combine like terms.

So, (p^2 + 4p - 23) - (3p^2 - 23p - 23) can be rewritten as:

= p^2 + 4p - 23 - 3p^2 + 23p + 23

= -2p^2 + 27p

Your answer is incorrect. You mistakenly subtracted the constants incorrectly and didn't combine the like terms accurately.

5. (5z - 2)(5z + 2)

To simplify this expression, you can use the formula for the difference of squares:

(a - b)(a + b) = a^2 - b^2

So, applying this formula to (5z - 2)(5z + 2):

= (5z)^2 - 2^2

= 25z^2 - 4

Your answer is correct!

6. (2m - 4)(m^2 + 2m + 4)

To simplify this expression, you can use the distributive property to multiply. Multiply each term of the first expression (2m - 4) by each term of the second expression (m^2 + 2m + 4). Then combine like terms if any.

So, (2m - 4)(m^2 + 2m + 4) can be expanded as:

= 2m * (m^2 + 2m + 4) - 4 * (m^2 + 2m + 4)

= 2m^3 + 4m^2 + 8m - 4m^2 - 8m - 16

= 2m^3

Your answer is correct!

7. (3x - 2)(2x - 3)

To simplify this expression, you can use the distributive property to multiply. Again, multiply each term of the first expression (3x - 2) by each term of the second expression (2x - 3). Then combine like terms if any.

So, (3x - 2)(2x - 3) can be expanded as:

= 3x * (2x - 3) - 2 * (2x - 3)

= 6x^2 - 9x - 4x + 6

= 6x^2 - 13x + 6

Your answer is correct!

So, out of the 7 expressions, you got 3 of them correct (3, 5, and 7). For the incorrect ones, I have explained the correct simplification process for each one.