Q. 43.7( 23 Votes )

Multiply the given polynomials.

i. 2x; x2 – 2x

ii. x5 – 1; x3 + 2x3 + 2

iii. 2y + 1; y2 – 2y3 + 3y

Answer :

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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