Do the following subtractions as directed.
Subtract $t^{4} - 3 t^{2} + 7$ from $5 t^{3} - 9$

t^{4} - 3 t^{2} - 5 t^{3} + 16

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- t^{4} - 5 t^{3} - 3 t^{2} + 16

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- t^{4} + 5 t^{3} + 3 t^{2} - 16

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t^{4} - 5 t^{3} - 3 t^{2} - 16

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Solution

The correct option is C $- t^{4} + 5 t^{3} + 3 t^{2} - 16$
We know that Like terms are terms that contain the same variables raised to the same power.

The only like term in the given expressions $t^{4} - 3 t^{2} + 7$ and $5 t^{3} - 9$ are $7$ and $- 9$ . So we group together the like terms and subtract $t^{4} - 3 t^{2} + 7$ from $5 t^{3} - 9$ as follows:

$(5 t^{3} - 9) - (t^{4} - 3 t^{2} + 7) = 5 t^{3} - 9 - t^{4} + 3 t^{2} - 7 = - t^{4} + 5 t^{3} + 3 t^{2} + (- 9 - 7) = - t^{4} + 5 t^{3} + 3 t^{2} - 16$

Hence, $(5 t^{3} - 9) - (t^{4} - 3 t^{2} + 7) = - t^{4} + 5 t^{3} + 3 t^{2} - 16$ .

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Similar questions

\int \frac{t^{4} - 3 t^{2} + 2}{t^{2} (1 + t^{2})}, d t

When we divide $3 t^{4} + 5 t^{3} - 7 t^{2} + 2 t + 2$ by $t^{2} + 3 t + 1$ , we get $3 t^{2} - 4 t + 2$ .

When we divide $3 t^{4} + 5 t^{3} - 7 t^{2} + 2 t + 2$ by $t^{2} + 3 t + 1$ , we get $3 t^{2} - 4 t + 2$ as quotient.

y = f (x)

x = g (t) = t^{5} - 5 t^{3} - 20 t + 7

y = h (t) = 4 t^{3} - 3 t^{2} - 18 t + 3, (- 2 < t < 2)

f (x)

y = f (x)

x = t^{5} - 5 t^{3} - 20 t + 7

y = 4 t^{3} - 3 t^{2} - 18 t + 3

t ϵ (- 2, 2)

f^{^{'}} (x)

t = 1

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