Adding and Subtracting Algebraic Expressions?

Question

Simplify.

1) 3r(-4rs^2)^2

2) a(a - 1)^2

3) 12x^2 - [x^2 - (2x^2 - 3)]

4) (5^3 x 5^2)/5^4

Answer 1

1. 3r(16r^2s^4)= 48r^3s^4

2. a(a^2-2a+1)=a^3-2a^2+a

3. 12x^2-x^2-2x^2+3=9x^2+3

4. (5^5)/5^4==3125/625=5(5^5/5^4=5^1=5)

Answer 2

[1] 3r(16)(r^2)(s^4)
48(r^3)(s^4)
48 r^3 s^4

[2] (a)(a^2 - 2a + 1)
a^3 -2^a + a

[3] 12x^2 - x^2 + 2x^2 - 3
13x^2 - 3
Note: - [ - (2x^2 - 3)] = 2x^2 - 3 watch the negative signs
If you are not sure of your answer, plug in x = 2
into both the original expression and the final answer
to make sure you get the same value or to catch errors.
Example: 12(2^2) - [2^2 - (2*2^2 - 3)] = 49
and 13(2^2) - 3 = 49 also, so this looks correct.

[4] (5^5) / 5^4 = 5^1 = 5
Note: I would reduce the fraction first instead of multiplying