What is (2/3 x+7)(4/7 x-6) ?

The solution to (2/3 x+7)(4/7 x-6) is (8x^2)/(21)-42

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simplify (2/3 x+7)(4/7 x-6)

simplify

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

\frac{8 x ^{2}}{21} - 42

Solution steps

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

Multiply

\frac{2}{3} x : \frac{2 x}{3}

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

Multiply

\frac{4}{7} x : \frac{4 x}{7}

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

Apply FOIL method:

(a + b) (c + d) = a c + a d + b c + b d

a = \frac{2 x}{3}, b = 7, c = \frac{4 x}{7}, d = - 6

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

Apply minus-plus rules

+ (- a) = - a

= \frac{2 x}{3} \cdot \frac{4 x}{7} - 6 \cdot \frac{2 x}{3} + 7 \cdot \frac{4 x}{7} - 7 \cdot 6

Simplify

\frac{2 x}{3} \cdot \frac{4 x}{7} - 6 \cdot \frac{2 x}{3} + 7 \cdot \frac{4 x}{7} - 7 \cdot 6 : \frac{8 x ^{2}}{21} - 42

= \frac{8 x ^{2}}{21} - 42

(3 x - 4 y) (3 x + 4 y)

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

\frac{4 x y ^{3}}{x ^{7} y ^{3}}

\frac{1}{6} n (n + 1) (2 n + 1)

\frac{7}{18}

What is (2/3 x+7)(4/7 x-6) ?
The solution to (2/3 x+7)(4/7 x-6) is (8x^2)/(21)-42