Topic: Factorisation Thswer the following: $$ 2 b(3 a-c)+12 a c-b^{2} $$ Factorise

Question

UpStudy AI · Accepted Answer

To factorize the expression:

$$ 2b(3a - c) + 12ac - b^2 $$

**Step 1: Expand the Expression**

First, distribute the $$2b$$ in the term $$2b(3a - c)$$:

$$
2b \cdot 3a = 6ab
$$
$$
2b \cdot (-c) = -2bc
$$

So, the expression becomes:

$$
6ab - 2bc + 12ac - b^2
$$

**Step 2: Rearrange the Terms**

Rearrange the expression to group like terms:

$$
6ab + 12ac - 2bc - b^2
$$

**Step 3: Factor by Grouping**

Group the terms as follows:

$$
(6ab + 12ac) + (-2bc - b^2)
$$

Factor out the common factors from each group:

- From the first group $$6ab + 12ac$$, factor out $$6a$$:
  
  $$
  6a(b + 2c)
  $$

- From the second group $$-2bc - b^2$$, factor out $$-b$$:

$$
  -b(2c + b) \quad \text{or} \quad -b(b + 2c)
  $$

So, the expression now looks like:

$$
6a(b + 2c) - b(b + 2c)
$$

**Step 4: Factor Out the Common Binomial**

Both terms contain the binomial $$(b + 2c)$$:

$$
(b + 2c)(6a - b)
$$

**Final Factored Form:**

$$
(6a - b)(b + 2c)
$$

**Answer:**

After factoring, the expression is (6 a – b) multiplied by (b + 2 c). Thus,

(6a − b)(b + 2c)
The factored form of the expression $$ 2b(3a - c) + 12ac - b^2 $$ is $$ (6a - b)(b + 2c) $$.

Topic: Factorisation Thswer the following: \( 2 b(3 a-c)+12 a c-b^{2} \) Factorise