Question

${y}^{3 } - 8 \div y - 2$
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Answer 1

Answer:

y² + 2y + 4

Step-by-step explanation:

1. Rewrite y³ - 8 in the form (a³ - b³) where a = y and b = 2

$\frac{y^3 - 2^3}{y - 2\\}$

2. Difference of cubes: a³ - b³ = (a - b)(a² + ab + b²)

$\frac{(y-2)(y^2+(y)(2)+2^2)}{y-2}$

3. Simplfy 2² to 4

$\frac{(y-2)(y^2+y*2+4}{y-2}$

4. Regroup Terms

$\frac{(y-2)(y^2+2y+4)}{y-2}$

5. Cancel out (y-2) by multiplying

$y^2 + 2y + 4$