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Question
Take away:
\[\frac{6}{5} x^2 - \frac{4}{5} x^3 + \frac{5}{6} + \frac{3}{2}x \text { from }\frac{x^3}{3} - \frac{5}{2} x^2 + \frac{3}{5}x + \frac{1}{4}\]
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Solution
The difference is given by:
\[\left( \frac{x^3}{3} - \frac{5}{2} x^2 + \frac{3}{5}x + \frac{1}{4} \right) - \left( \frac{6}{5} x^2 - \frac{4}{5} x^3 + \frac{5}{6} + \frac{3}{2}x \right)\]
\[ = \frac{x^3}{3} - \frac{5}{2} x^2 + \frac{3}{5}x + \frac{1}{4} - \frac{6}{5} x^2 + \frac{4}{5} x^3 - \frac{5}{6} - \frac{3}{2}x\]
\[= \frac{x^3}{3} + \frac{4}{5} x^3 - \frac{5}{2} x^2 - \frac{6}{5} x^2 + \frac{3}{5}x - \frac{3}{2}x + \frac{1}{4} - \frac{5}{6}\] (Collecting like terms)
\[\left( \frac{5 + 12}{15} \right) x^3 + \left( \frac{- 25 - 12}{10} \right) x^2 + \left( \frac{6 - 15}{10} \right)x + \left( \frac{6 - 20}{24} \right)\]
\[= \frac{17}{15} x^3 - \frac{37}{10} x^2 - \frac{9}{10}x - \frac{7}{12}\] (Combining like terms)
RELATED QUESTIONS
State whether a given pair of term is of like or unlike term.
1,100
State whether a given pair of term is of like or unlike term.
14xy, 42yx
Identify like term in the following:
−xy2, − 4yx2, 8x2, 2xy2, 7y, −11x2, −100x, −11yx, 20x2y, −6x2, y, 2xy, 3x
Take away:
\[\frac{7}{4} x^3 + \frac{3}{5} x^2 + \frac{1}{2}x + \frac{9}{2}\text { from } \frac{7}{2} - \frac{x}{3} - \frac{x^2}{5}\]
Simplify the following:
x2 − 3x + 5 − \[\frac{1}{2}\] (3x2 − 5x + 7)
Simplify the following:
\[\frac{11}{2} x^2 y - \frac{9}{4}x y^2 + \frac{1}{4}xy - \frac{1}{14} y^2 x + \frac{1}{15}y x^2 + \frac{1}{2}xy\]
Simplify the following: \[- \frac{1}{2} a^2 b^2 c + \frac{1}{3}a b^2 c - \frac{1}{4}ab c^2 - \frac{1}{5}c b^2 a^2 + \frac{1}{6}c b^2 a - \frac{1}{7} c^2 ab + \frac{1}{8}c a^2 b .\]
2pq and – 7qp are like terms
Identify the like terms: 12x3y2z, – y3x2z, 4z3y2x, 6x3z2y, – 5y3x2z
5a and 5b are unlike terms.
