Question

) (a+b) +(a-b): 2) 3(2-a +4 (a-5). 3) (x-1)^3-(x+1)^3. 4) -(3+x)^2+(1-x)^2​

Answer 1

1. (a+b)+(a-b)=a+b+a-b=2a
2. 3(2-a+4(a-5)=3(2-a+4a-20)=3(3a-18)=9a-54
3. (x-1)³- (x+1)³= x³-3x²+3x-1-x³-3x²-3x-1=-3x²-1-3x²-1=-6x²-2
4. -(3+x)²+(1-x)²=-(9+6x+x²)+1-2x+x²=-9-6x-x²+1-2x+x²=-8x-8

Answer 2

Let's simplify each of the given expressions:

1. (a+b) + (a-b): By applying the distributive property, we can simplify this expression as follows: (a + b) + (a - b) = a + b + a - b

   Now, combining like terms, we get: a + a + b - b

   Finally, simplifying further, we have: 2a

Therefore, the simplified form of (a+b) + (a-b) is 2a.

2. 3(2-a + 4(a-5)): Using the distributive property, we can simplify this expression as follows: 3(2 - a) + 3(4(a - 5))

   Expanding, we have: 6 - 3a + 12(a - 5)

   Distributing further, we get: 6 - 3a + 12a - 60

   Combining like terms, we have: (12a - 3a) + (6 - 60) 9a - 54

Therefore, the simplified form of 3(2 - a + 4(a - 5)) is 9a - 54.

3. (x-1)^3 - (x+1)^3: Using the formula for the difference of cubes, we can simplify this expression as follows: (x - 1)^3 - (x + 1)^3 = (x - 1 - (x + 1))((x - 1)^2 + (x - 1)(x + 1) + (x + 1)^2)

   Simplifying further, we have: (-2)((x - 1)^2 + (x^2 - 1) + (x + 1)^2)

   Expanding the squares, we get: (-2)((x^2 - 2x + 1) + (x^2 - 1) + (x^2 + 2x + 1))

   Combining like terms, we have: (-2)(3x^2 + 1)

Therefore, the simplified form of (x - 1)^3 - (x + 1)^3 is -2(3x^2 + 1).

4. -(3 + x)^2 + (1 - x)^2: Expanding the squares and simplifying, we have: -(9 + 6x + x^2) + (1 - 2x + x^2)

   Combining like terms, we get: -9 - 6x - x^2 + 1 - 2x + x^2

   Simplifying further, we have: (-x^2 - 8x - 8)

Therefore, the simplified form of -(3 + x)^2 + (1 - x)^2 is -x^2 - 8x - 8.