**Factoring expressions :**

Factoring (called "Factorising" in the UK) is the process of finding the factors.

It is like "splitting" an expression into a multiplication of simpler expressions.

**Step 1 : **

Find the largest common divisor for all the terms in the expression

**Step 2 : **

Divide each term of the expression by the largest common divisor.

**Step 3: **

Write the quotients inside the parenthesis.

**Step 4 : **

Write the largest common divisor and the parenthesis together using multiplication.

**Example 1 : **

Factor : 4x + 8

**Solution : **

**Step 1 : **

Find the largest common divisors for 4x and 8.

The largest common divisor for 4x and 8 is 4.

**Step 2 : **

Divide 4x and 8 by 4

4x / 4 = x and 8 / 4 = 2

**Step 3 :**

Write the quotients x and 2 inside the parenthesis and multiply by the largest common divisor 4.

4(x + 2)

Hence, 4x + 8 = 4(x + 2)

**Justify and Evaluate : **

To verify our answer, let us use distributive property to multiply 4 and (x+2).

Distribute 4 to x and 2.

4(x+2) = 4.x + 4.2

4(x+2) = 4x + 8

When we multiply 4 and (x + 2), we get the expression given in the question. So, 4 and (x+2) are the factors of 4x + 8

**Example 2 : **

Factor : 16a + 64b - 4c

**Solution : **

**Step 1 : **

Find the largest common divisors for 16a, 64b and 4c.

The largest common divisor for 16a, 64b and 4c is 4.

**Step 2 :**

Divide 16a, 64b and 4c by 4

16a / 4 = 4a, 64b / 4 = 16b and 4c / 4 = c

**Step 3 :**

Write the quotients 4a, 16b and c inside the parenthesis and multiply by the largest common divisor 4.

4(4a + 16b - c)

Hence, 16a + 64b - 4c = 4(4a + 16b - c)

**Justify and Evaluate :**

To verify our answer, let us use distributive property to multiply 4 and (4a + 16b - c).

Distribute 4 to 4a, 16b and c.

4(4a + 16b - c) = 4.4a + 4.16b - 4.c

4(4a + 16b - c) = 16a + 64b - 4c

When we multiply 4 and (4a+16b-c), we get the expression given in the question. So, 4 and (4a+16b-c) are the factors of 16a + 64b - 4c

**Example 3 : **

Factor : 5x² - 15x

**Solution : **

**Step 1 : **

Find the largest common divisors for 5x² and 15x.

The largest common divisor for 5x² and 15x is 5x.

**Step 2 :**

Divide 5x² and 15x by 5x

5x² / 5x = x and 15x / 5x = 3

**Step 3 :**

Write the quotients x and 3 inside the parenthesis and multiply by the largest common divisor 5x.

(5x)(x - 3)

Hence, 5x² + 15x = (5x)(x - 3)

**Justify and Evaluate :**

To verify our answer, let us use distributive property to multiply 5x and (x - 3).

Distribute 5x to x and 3.

(5x)(x - 3) = 5x.x - 5x.3

(5x)(x - 3) = 5x² - 15x

When we multiply 5x and (x-3), we get the expression given in the question. So, 5x and (x-3) are the factors of 5x² - 15x.

After having gone through the stuff given above, we hope that the students would have understood "Factoring expressions".

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