# Multiply the given polynomials.i. 2x; x2 – 2xii. x5 – 1; x3 + 2x3 + 2iii. 2y + 1; y2 – 2y3 + 3y

The multiplication is as follows:

2x × (x2 – 2x – 1)

2x.x2 – 2x.2x – 2x.1

2x2+1 – 4x1+1 – 2x

2x3 – 4x2 – 2x

Therefore, the product = 2x3 – 4x2 – 2x

“.” represents multiplication

ii. The multiplication is as follows:

(x5 – 1) × (x3 + 2x3 + 2)

x5.x3 + 2x3.x5 + 2.x5 – 1.x3 – 1.2x3 – 1.2

x5+3 + 2x3 + 5 +2x5 – x3 – 2x3 – 2

x8 + 2x8 + 5 + 2x5 – x3 – 2x3 – 2

3x8 + 2x5 + 3x3 + 3

The product is = 3x8 + 2x5 + 3x3 + 3

“.” represents multiplication

iii. The multiplication is as follows:

(2y + 1) × (y2 – 2y3 + 3y)

2y.y2 – 2y3.2y + 3y.2y + 1.y2 – 1.2y3 + 1.3y

2y2+1 – 4y3+1 + 6y1+1 + y2 – 2y3 + 3y

2y3 – 4y4 + 6y2 + y2 – 2y3 + 3y

-4y4 + 7y2 + 3y

The product is = -4y4 + 7y2 + 3y

“.” represents multiplication

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