Rewrite the expression in long division form .

Divide the first term of the dividend by the first term of the divisor

So the first term of the quotient is y⁴. Multiply the (y – 2) by y⁴ and subtract.

Divide the first term of the next row by the first term of the divisor .

So the first term of the quotient is 2y³. Multiply the (y – 2) by 2y³ and subtract.

Divide the first term of the next row by the first term of the divisor

So the first term of the quotient is 4y². Multiply the (y – 2) by 4y² and subtract.

Divide the first term of the next row by the first term of the divisor .

So the first term of the quotient is 5y. Multiply the (y – 2) by 5y and subtract.

Divide the first term of the next row by the first term of the divisor .

So the first term of the quotient is 10. Multiply the (y – 2) by 10 and subtract.

The quotient is  , and the remainder is 0. Therefore,

.