Question

7x³ + y³+2z from 12x³-8y+z³+8

Answer 1

To simplify the expression 7x³ + y³ + 2z divided by 12x³ - 8y + z³ + 8, you can perform polynomial division. Here are the steps:

Divide the highest-degree term in the numerator (7x³) by the highest-degree term in the denominator (12x³).

7x³ ÷ 12x³ = (7/12)

Now, multiply the denominator by (7/12):

(7/12) * (12x³ - 8y + z³ + 8) = 7x³ - (7/12) * 8y + (7/12) * z³ + (7/12) * 8

Perform the same steps for the y³ term:

y³ ÷ 12x³ = (1/12x³)

Multiply the denominator by (1/12x³):

(1/12x³) * (12x³ - 8y + z³ + 8) = 1 - (1/12) * (8y/x³) + (1/12) * (z³/x³) + (1/12) * 8/x³

Finally, for the 2z term:

2z ÷ 12x³ = (1/6x³)

Multiply the denominator by (1/6x³):

(1/6x³) * (12x³ - 8y + z³ + 8) = 2 - (1/6) * (8y/x³) + (1/6) * (z³/x³) + (1/6) * 8/x³

Now, combine all the terms to simplify the expression:

(7/12) * 12x³ - (7/12) * 8y + (7/12) * z³ + (7/12) * 8 + (1/12x³) * 12x³ - (1/12) * (8y/x³) + (1/12) * (z³/x³) + (1/12) * 8/x³ + (1/6x³) * 12x³ - (1/6) * (8y/x³) + (1/6) * (z³/x³) + (1/6) * 8/x³

Simplify each term:

7x³ - (7/12) * 8y + (7/12) * z³ + (7/12) * 8 + 1 - (1/12) * (8y/x³) + (1/12) * (z³/x³) + (1/12) * 8/x³ + 2 - (1/6) * (8y/x³) + (1/6) * (z³/x³) + (1/6) * 8/x³

Now, combine like terms if possible, and you have your simplified expression.

Explanation:

Answer 2

y³ - 2z

Explanation:

To simplify the expression 7x³ + y³ + 2z from 12x³ - 8y + z³ + 8, we combine like terms:

12x³ - 8y + z³ + 8

Since there is no like term for 7x³ + y³ + 2z, we can rewrite the expression as:

(12x³ - 8y + z³ + 8) - (12x³ - 7x³ + 8y - y³ - z³ + 2z)

Simplifying further:

12x³ - 8y + z³ + 8 - 12x³ + 7x³ - 8y + y³ + z³ - 2z

Combining like terms:

(-12x³ + 12x³) + (-8y + 8y) + (z³ + z³) + (y³) + (-2z)

The terms -12x³ + 12x³, -8y + 8y, and z³ + z³ simplify to 0, and we are left with:

y³ - 2z

Therefore, the simplified expression is y³ - 2z.