Match the following-Column - IColumn - IIP x2 - 5x3 - 3 - 51 -x3 - 3x2 - 3x - 2Q -103xy3 - 65x3y2 -x3 - x2 - 3x - 6R x3 - x2 - x - 2 - 2x3 - 2x2 - 4x - 43 x5 - 5x3 - 3x2 - 20S x3 - x2 - x - 2 - 2x2 - 2x3 - 4x - 44 -4x4y4

The correct option is B (P) → (3), (Q) → (4), (R) → (1), (S) → (2)(P) (x^2 + 5)(x^3 + 3) + 5 = x^6 + 3x^2 + 5x^3 + 15 + 5 = ...

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Byju's Answer

Standard VIII

Mathematics

Multiplication of Any Polynomial

Match the fol...

Question

Match the following.
Column - I Column - II
(P) $(x^{2} + 5) (x^{3} + 3) + 5$ (1) ${- x}^{3} - 3 x^{2} + 3 x + 2$
(Q) $(\frac{- 10}{3} x y^{3}) \times (\frac{6}{5} x^{3} y)$ (2) $- x^{3} + x^{2} + 3 x - 6$
(R) $(x^{3} - x^{2} - x - 2) - (2 x^{3} + 2 x^{2} - 4 x - 4)$ (3) $x^{5} + 5 x^{3} + 3 x^{2} + 20$
(S) $(x^{3} - x^{2} - x - 2) + (2 x^{2} - 2 x^{3} + 4 x - 4)$ (4) $- 4 x^{4} y^{4}$

(P)

\to

(1), (Q)

\to

(2), (R)

\to

(3), (S)

\to

(4)

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(P)

\to

(3), (Q)

\to

(4), (R)

\to

(1), (S)

\to

(2)

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(P)

\to

(4), (Q)

\to

(1), (R)

\to

(3), (S)

\to

(2)

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(P)

\to

(3), (Q)

\to

(4), (R)

\to

(2), (S)

\to

(1)

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Solution

The correct option is B (P) $\to$ (3), (Q) $\to$ (4), (R) $\to$ (1), (S) $\to$ (2)
(P) $(x^{2} + 5) (x^{3} + 3) + 5$
= $x^{6} + 3 x^{2} + 5 x^{3} + 15 + 5$
= $x^{5} + 5 x^{3} + 3 x^{2} + 20$

(Q) $(\frac{- 10}{3} x y^{3}) \times (\frac{6}{5} x^{3} y)$
= $(\frac{- 10}{3} \times \frac{6}{5}) x^{4} y^{4}$ = $- 4 x^{4} y^{4}$

(R) $(x^{3} - x^{2} - x - 2) - (2 x^{3} + 2 x^{2} - 4 x - 4)$
= $x^{3} - x^{2} - x - 2 - 2 x^{3} - 2 x^{2} + 4 x + 4$
= $- x^{3} - 3 x^{2} + 3 x + 2$

(S) $(x^{3} - x^{2} - x - 2) + (2 x^{2} - 2 x^{3} + 4 x - 4)$
= $x^{3} - x^{2} - x - 2 + 2 x^{2} - 2 x^{3} + 4 x - 4$
= $- x^{3} + x^{2} + 3 x - 6$

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	Column - I		Column - II
(P)	$(x^{2} + 5) (x^{3} + 3) + 5$	(1)	${- x}^{3} - 3 x^{2} + 3 x + 2$
(Q)	$(\frac{- 10}{3} x y^{3}) \times (\frac{6}{5} x^{3} y)$	(2)	$- x^{3} + x^{2} + 3 x - 6$
(R)	$(x^{3} - x^{2} - x - 2) - (2 x^{3} + 2 x^{2} - 4 x - 4)$	(3)	$x^{5} + 5 x^{3} + 3 x^{2} + 20$
(S)	$(x^{3} - x^{2} - x - 2) + (2 x^{2} - 2 x^{3} + 4 x - 4)$	(4)	$- 4 x^{4} y^{4}$

Match the following.Column - IColumn - II(P)(x2+5)(x3+3)+5(1)−x3−3x2+3x+2(Q)(−103xy3)×(65x3y)(2)−x3+x2+3x−6(R)(x3−x2−x−2)−(2x3+2x2−4x−4)(3)x5+5x3+3x2+20(S)(x3−x2−x−2)+(2x2−2x3+4x−4)(4)−4x4y4