Resolved: "To calculate: To factor the expression 43x13(2x−3)+2x43."

Secondary
Algebra
Algebra II
Rational exponents and radicals

Josalynn

Answered question

2021-10-22

To calculate: To factor the expression

\frac{4}{3} x^{\frac{1}{3}} (2 x - 3) + 2 x^{\frac{4}{3}}

Answer & Explanation

Obiajulu

Skilled2021-10-23Added 98 answers

Calculation:
This can be written as

\frac{4}{3} x^{\frac{1}{3}} (2 x - 3) + 2 x^{\frac{4}{3}} = 2 \cdot \frac{2}{3} \cdot x^{\frac{1}{3}} \cdot (2 x - 3) + 2 \cdot x^{\frac{1}{3}} \cdot x

Factoring out the common terms i.e. 2 and

x^{\frac{1}{3}}

\frac{4}{3} x^{\frac{1}{3}} (2 x - 3) + 2 x^{\frac{4}{3}} = 2 \cdot x^{\frac{1}{3}} \cdot (\frac{2}{3} (2 x - 3) + x)

\frac{4}{3} x^{\frac{1}{3}} (2 x - 3) + 2 x^{\frac{4}{3}} = 2 x^{\frac{1}{3}} (\frac{2}{3} \cdot 2 x - \frac{2}{3} \cdot 3 + x)

\frac{4}{3} x^{\frac{1}{3}} (2 x - 3) + 2 x^{\frac{4}{3}} = 2 x^{\frac{1}{3}} (\frac{4 x}{3} - \frac{6}{3} + x)

\frac{4}{3} x^{\frac{1}{3}} (2 x - 3) + 2 x^{\frac{4}{3}} = 2 x^{\frac{1}{3}} (\frac{4 x}{3} - \frac{6}{3} + \frac{3 x}{3})

\frac{4}{3} x^{\frac{1}{3}} (2 x - 3) + 2 x^{\frac{4}{3}} = 2 x^{\frac{1}{3}} (\frac{7 x}{3} - \frac{6}{3})

\frac{4}{3} x^{\frac{1}{3}} (2 x - 3) + 2 x^{\frac{4}{3}} = 2 x^{\frac{1}{3}} (\frac{7 x - 6}{3})

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