What is expand 5r^2s^3(-2r^2+3rs-4s^2) ?

The solution to expand 5r^2s^3(-2r^2+3rs-4s^2) is -10r^4s^3+15r^3s^4-20r^2s^5

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expand 5r^2s^3(-2r^2+3rs-4s^2)

expand

5 r^{2} s^{3} (- 2 r^{2} + 3 rs - 4 s^{2})

- 10 r^{4} s^{3} + 15 r^{3} s^{4} - 20 r^{2} s^{5}

Solution steps

5 r^{2} s^{3} (- 2 r^{2} + 3 rs - 4 s^{2})

Apply the distributive law:

m (a + b + c) = ma + mb + m c

5 r^{2} s^{3} (- 2 r^{2} + 3 rs - 4 s^{2}) = 5 r^{2} s^{3} (- 2 r^{2}) + 5 r^{2} s^{3} \cdot 3 rs + 5 r^{2} s^{3} (- 4 s^{2})

= 5 r^{2} s^{3} (- 2 r^{2}) + 5 r^{2} s^{3} \cdot 3 rs + 5 r^{2} s^{3} (- 4 s^{2})

Simplify

5 r^{2} s^{3} (- 2 r^{2}) + 5 r^{2} s^{3} \cdot 3 rs + 5 r^{2} s^{3} (- 4 s^{2}) : - 10 r^{4} s^{3} + 15 r^{3} s^{4} - 20 r^{2} s^{5}

= - 10 r^{4} s^{3} + 15 r^{3} s^{4} - 20 r^{2} s^{5}

9 (3 x)

7 sec^{2} (x) - 7 tan^{2} (x)

- 5 m - 3 n + 6 + 2 m + 2 n - 8

(\frac{3}{- 3})^{4}

What is expand 5r^2s^3(-2r^2+3rs-4s^2) ?
The solution to expand 5r^2s^3(-2r^2+3rs-4s^2) is -10r^4s^3+15r^3s^4-20r^2s^5