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Mathematics

How much is x3 - 3x2 + 5x - 2 less than 3 - 2x + x2 - x3?

Algebraic Expressions

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Answer

Here it asks "how much is A less than B," it means B is the larger value. Therefore, we subtract A from B (B - A).

∴ Subtract (x3 - 3x2 + 5x - 2) from (3 - 2x + x2 - x3)

Arranging the expressions in ascending powers of x (constant, x, x2, x3).

3−2x+x2−x3−2+5x−3x2+x3+2−+−5−7x+4x2−2x3\begin{array}{rcccccc} 3 & - & 2x & + & x^2 & - & x^3 \\ -2 & + & 5x & - & 3x^2 & + & x^3 \\ +\phantom{2} & - & & + & & - \\ \hline 5 & - & 7x & + & 4x^2 & - & 2x^3 \\ \hline \end{array}

Hence, the answer is 5 - 7x + 4x2 - 2x3

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