#
factorise

27p3-125q3

## Answers

**Answer:**

(3p - 5q) • (9p2 + 15pq + 25q2)

**Step-by-step explanation:**

Factoring: 27p3-125q3

Theory : A difference of two perfect cubes, a3 - b3 can be factored into

(a-b) • (a2 +ab +b2)

Proof : (a-b)•(a2+ab+b2) =

a3+a2b+ab2-ba2-b2a-b3 =

a3+(a2b-ba2)+(ab2-b2a)-b3 =

a3+0+0+b3 =

a3+b3

Check : 27 is the cube of 3

Check : 125 is the cube of 5

Check : p3 is the cube of p1

Check : q3 is the cube of q1

Factorization is :

(3p - 5q) • (9p2 + 15pq + 25q2)

**Step-by-step explanation:**

**Given**:

**To find**: Factorise.

**Solution:**

__Identity used:__

### Step 1: Convert given polynomial in standard form.

### Step 2: Apply identity to factorise.

simply

**Final answer:**

Hope it helps you.

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