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Simplify: 6(x3−2x2+3x)−(x3+2x−3).6(x^3-2x^2+3x)-(x^3+2x-3).6(x3−2x2+3x)−(x3+2x−3).​​
Question

Simplify: 6(x32x2+3x)(x3+2x3).6(x^3-2x^2+3x)-(x^3+2x-3).​​

A.

5x312x2+16x35x^3-12x^2+16x-3​​

B.

5x312x2+16x+35x^3-12x^2+16x+3​​

C.

5x3+12x2+16x35x^3+12x^2+16x-3​​

D.

5x3+12x2+16x+35x^3+12x^2+16x+3​​

Correct option is B

Given:

Expression to simplify:

6(x32x2+3x)(x3+2x3)6(x^3 - 2x^2 + 3x) - (x^3 + 2x - 3)​​

Property Used:

Distributive Property: a(b + c) = ab + ac

Solution:

Expand the terms using distributive property.

Expand 6(x32x2+3x):6(x^3 - 2x^2 + 3x):​​

6x312x2+18x6x^3 - 12x^2 + 18x​​

Expand  (x3+2x3):-(x^3 + 2x - 3):​​

x32x+3-x^3 - 2x + 3​​

Combine both terms

The simplified expression is: 5x312x2+16x+35x^3 - 12x^2 + 16x + 3​​

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