Pre-Algebra Examples

$16 m {(r + t)}^{3}$ , $4 p {(r + t)}^{4}$

Step 1

Simplify each term.

Tap for more steps...

Use the Binomial Theorem.

$16 m (r^{3} + 3 r^{2} t + 3 r t^{2} + t^{3}), 4 p {(r + t)}^{4}$

Apply the distributive property.

$16 m r^{3} + 16 m (3 r^{2} t) + 16 m (3 r t^{2}) + 16 m t^{3}, 4 p {(r + t)}^{4}$

Simplify.

Tap for more steps...

Multiply $3$ by $16$ .

$16 m r^{3} + 48 m (r^{2} t) + 16 m (3 r t^{2}) + 16 m t^{3}, 4 p {(r + t)}^{4}$

Multiply $3$ by $16$ .

$16 m r^{3} + 48 m (r^{2} t) + 48 m (r t^{2}) + 16 m t^{3}, 4 p {(r + t)}^{4}$

Remove parentheses.

$16 m r^{3} + 48 m r^{2} t + 48 m r t^{2} + 16 m t^{3}, 4 p {(r + t)}^{4}$

Use the Binomial Theorem.

$16 m r^{3} + 48 m r^{2} t + 48 m r t^{2} + 16 m t^{3}, 4 p (r^{4} + 4 r^{3} t + 6 r^{2} t^{2} + 4 r t^{3} + t^{4})$

Apply the distributive property.

$16 m r^{3} + 48 m r^{2} t + 48 m r t^{2} + 16 m t^{3}, 4 p r^{4} + 4 p (4 r^{3} t) + 4 p (6 r^{2} t^{2}) + 4 p (4 r t^{3}) + 4 p t^{4}$

Simplify.

Tap for more steps...

Multiply $4$ by $4$ .

$16 m r^{3} + 48 m r^{2} t + 48 m r t^{2} + 16 m t^{3}, 4 p r^{4} + 16 p (r^{3} t) + 4 p (6 r^{2} t^{2}) + 4 p (4 r t^{3}) + 4 p t^{4}$

Multiply $6$ by $4$ .

$16 m r^{3} + 48 m r^{2} t + 48 m r t^{2} + 16 m t^{3}, 4 p r^{4} + 16 p (r^{3} t) + 24 p (r^{2} t^{2}) + 4 p (4 r t^{3}) + 4 p t^{4}$

Multiply $4$ by $4$ .

$16 m r^{3} + 48 m r^{2} t + 48 m r t^{2} + 16 m t^{3}, 4 p r^{4} + 16 p (r^{3} t) + 24 p (r^{2} t^{2}) + 16 p (r t^{3}) + 4 p t^{4}$

Remove parentheses.

$16 m r^{3} + 48 m r^{2} t + 48 m r t^{2} + 16 m t^{3}, 4 p r^{4} + 16 p r^{3} t + 24 p r^{2} t^{2} + 16 p r t^{3} + 4 p t^{4}$

Step 2

Factor out the GCF of $4$ from $16 m r^{3} + 48 m r^{2} t + 48 m r t^{2} + 16 m t^{3} + 4 p r^{4} + 16 p r^{3} t + 24 p r^{2} t^{2} + 16 p r t^{3} + 4 p t^{4}$ .

Tap for more steps...

Factor out the GCF of $4$ from each term in the polynomial.

Tap for more steps...

Factor out the GCF of $4$ from the expression $16 m r^{3}$ .

$4 (4 m r^{3}) + 48 m r^{2} t + 48 m r t^{2} + 16 m t^{3} + 4 p r^{4} + 16 p r^{3} t + 24 p r^{2} t^{2} + 16 p r t^{3} + 4 p t^{4}$

Factor out the GCF of $4$ from the expression $48 m r^{2} t$ .

$4 (4 m r^{3}) + 4 (12 m r^{2} t) + 48 m r t^{2} + 16 m t^{3} + 4 p r^{4} + 16 p r^{3} t + 24 p r^{2} t^{2} + 16 p r t^{3} + 4 p t^{4}$

Factor out the GCF of $4$ from the expression $48 m r t^{2}$ .

$4 (4 m r^{3}) + 4 (12 m r^{2} t) + 4 (12 m r t^{2}) + 16 m t^{3} + 4 p r^{4} + 16 p r^{3} t + 24 p r^{2} t^{2} + 16 p r t^{3} + 4 p t^{4}$

Factor out the GCF of $4$ from the expression $16 m t^{3}$ .

$4 (4 m r^{3}) + 4 (12 m r^{2} t) + 4 (12 m r t^{2}) + 4 (4 m t^{3}) + 4 p r^{4} + 16 p r^{3} t + 24 p r^{2} t^{2} + 16 p r t^{3} + 4 p t^{4}$

Factor out the GCF of $4$ from the expression $4 p r^{4}$ .

$4 (4 m r^{3}) + 4 (12 m r^{2} t) + 4 (12 m r t^{2}) + 4 (4 m t^{3}) + 4 (p r^{4}) + 16 p r^{3} t + 24 p r^{2} t^{2} + 16 p r t^{3} + 4 p t^{4}$

Factor out the GCF of $4$ from the expression $16 p r^{3} t$ .

$4 (4 m r^{3}) + 4 (12 m r^{2} t) + 4 (12 m r t^{2}) + 4 (4 m t^{3}) + 4 (p r^{4}) + 4 (4 p r^{3} t) + 24 p r^{2} t^{2} + 16 p r t^{3} + 4 p t^{4}$

Factor out the GCF of $4$ from the expression $24 p r^{2} t^{2}$ .

$4 (4 m r^{3}) + 4 (12 m r^{2} t) + 4 (12 m r t^{2}) + 4 (4 m t^{3}) + 4 (p r^{4}) + 4 (4 p r^{3} t) + 4 (6 p r^{2} t^{2}) + 16 p r t^{3} + 4 p t^{4}$

Factor out the GCF of $4$ from the expression $16 p r t^{3}$ .

$4 (4 m r^{3}) + 4 (12 m r^{2} t) + 4 (12 m r t^{2}) + 4 (4 m t^{3}) + 4 (p r^{4}) + 4 (4 p r^{3} t) + 4 (6 p r^{2} t^{2}) + 4 (4 p r t^{3}) + 4 p t^{4}$

Factor out the GCF of $4$ from the expression $4 p t^{4}$ .

$4 (4 m r^{3}) + 4 (12 m r^{2} t) + 4 (12 m r t^{2}) + 4 (4 m t^{3}) + 4 (p r^{4}) + 4 (4 p r^{3} t) + 4 (6 p r^{2} t^{2}) + 4 (4 p r t^{3}) + 4 (p t^{4})$

Since all the terms share a common factor of $4$ , it can be factored out of each term.

$4 (4 m r^{3} + 12 m r^{2} t + 12 m r t^{2} + 4 m t^{3} + p r^{4} + 4 p r^{3} t + 6 p r^{2} t^{2} + 4 p r t^{3} + p t^{4})$

Step 3

The greatest common factor $GCF$ is the term in front of the factored expression.

$4$