Step-by-step explanation:

Question:

Assuming your question is this: FACTORISE:

• 4a² + 20a + 25
• 9a² + 6a + 1
• 9x² + 12x + 4

Answer:

1. 4a² + 20a + 25

Ans: 4a² + 20a + 25.

Multiply the first coefficient with second. I.e. = 4 × 25 = 100.

Now find two factor from 100 that sum up to 20(a)

• 10 + 10 = 20

4a² + (10 + 10)a + 25

4a² + (10a + 10a) + 25

4a² + 10a + 10a + 25

2a(2a + 5) + 5(2a + 5)

(2a + 5)(2a + 5) = (2a + 5)²

2. 9a² + 6a + 1

Ans: 9a² + 6a + 1

Multiply the first coefficient with second. I.e. = 9 × 1 = 9

Now find two factor from 9 that sum up to 6(a)

• 3 + 3 = 6

9a² + (3 + 3)a + 1

9a² + (3a + 3a) + 1

9a² + 3a + 3a + 1

3a(3a + 1) + 1(3a + 1)

(3a + 1)(3a + 1) = (3a + 1)²

3. 9x² + 12x + 4

Ans: 9x² + 12x + 4

Multiply the first coefficient with second. I.e. = 9 × 4 = 36

Now find two factors from 36 that sum up to 12(x)

• 6 + 6 = 12

9x² + (6 + 6)x + 4

9x² + (6x + 6x) + 4

9x² + 6x + 6x + 4

3x(3x + 2) + 2(3x + 2)

(3x + 2)(3x + 2) = (3x + 2)²