factor t^4-p^4 — step-by-step solution | Explain MAths

factor t^4-p^4

Let's factor in

ℝ

:

t^{4} - p^{4}

For

t^{4} - p^{4}

, we recognize a difference of two squares:

{(t^{2})}^{2} - {(p^{2})}^{2}

. Apply

a^{2} - b^{2} = (a - b) \cdot (a + b)

, with

a = t^{2}

and

b = p^{2}

You can factor:

t^{4} - p^{4}

into:

(t^{2} - p^{2}) \cdot (t^{2} + p^{2})

Let's factor in

ℝ

:

(t^{2} - p^{2}) \cdot (t^{2} + p^{2})

⇥Let's factorize in

ℝ

:

(t^{2} - p^{2})

⇥For

t^{2} - p^{2}

, we recognize a difference of two squares:

t^{2} - p^{2}

. Apply

a^{2} - b^{2} = (a - b) \cdot (a + b)

, with

a = t

and

b = p

⇥You can factor:

t^{2} - p^{2}

into:

(t - p) \cdot (t + p)

▷The factor

(t^{2} - p^{2})

factors as:

(p + t) \cdot (t - p)

⇥Let's factor in

ℝ

:

(t^{2} + p^{2})

⇥Factor found:

p^{2} + t^{2}

▶Factored expression:

(p + t) \cdot (t - p) \cdot (p^{2} + t^{2})