Factor by Grouping 40-5t^3

$40 - 5 t^{3}$

Step 1

Factor out the GCF of $5$ from $40 - 5 t^{3}$ .

Factor out the GCF of $5$ from each term in the polynomial.

Factor out the GCF of $5$ from the expression $40$ .

$5 (8) - 5 t^{3}$

Factor out the GCF of $5$ from the expression $- 5 t^{3}$ .

$5 (8) + 5 (- t^{3})$

Since all the terms share a common factor of $5$ , it can be factored out of each term.

$5 (8 - t^{3})$

Step 2

Rewrite $8$ as $2^{3}$ .

$5 (2^{3} - t^{3})$

Step 3

Since both terms are perfect cubes, factor using the difference of cubes formula, $a^{3} - b^{3} = (a - b) (a^{2} + a b + b^{2})$ where $a = 2$ and $b = t$ .

$5 ((2 - t) (2^{2} + 2 t + t^{2}))$

Step 4

Raise $2$ to the power of $2$ .

$5 ((2 - t) (4 + 2 t + t^{2}))$

Factor by Grouping 40-5t^3

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