Question

factorise : 125
p3+q3​

Answer 1

Answer:

125 = 5³

p³+q³ = (p+q)(p²+q²-pq)

hope it helps......

Answer 2

Step-by-step explanation:

Given: $125 {p}^{3} + {q}^{3}$

To find: Factorise.

Solution:

Identity used:

$\boxed{\bf {x}^{3} + {y}^{3} = (x + y)( {x}^{2} - xy + {y}^{2} ) }$

Step 1: Convert given polynomial in standard form.

$125 {p}^{3} + {q}^{3} = ( {5p)}^{3} + {q}^{3}$

Step 2: Apply identity to factorise.

$( {5p)}^{3} + {q}^{3} = (5p + q)( {(5p)}^{2} - 5p(q) + {q}^{2} )$

simply

$( {5p)}^{3} + {q}^{3} = (5p + q)( {25p}^{2} - 5pq + {q}^{2} )$

Final answer:

$\bf {125p}^{3} + {q}^{3} = (5p + q)( {25p}^{2} - 5pq + {q}^{2} )$

Hope it helps you.

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