How to factorise 84-2r-2r square ?

Question

Answer

84-r-2r^2=0
2r+2r-84=0
Dividing the equation by 2
r^2-r-42=0
r^2+7r-6r-42=0
r(r+7)-6(r+7)
(r+7)(r-6)=0
.

Answer

Hi!

I've used the 'splitting the middle term' method to factorize.

First, arrange the polynomial in order of its powers(descending).

We get -2r^2-2r+84.

(rest is in the attachment)

As a result we get (r-14)(r+12).

Hope this helped,

have a nice day!

Answer

Factorizing 84-2r-2r square

To factorize the expression 84-2r-2r square, we need to identify common factors and use algebraic techniques such as factoring by grouping or using the difference of squares formula. Let's break down the process step by step:

Step 1: Identify common factors
In the given expression, there are no common factors present. Therefore, we move on to the next step.

Step 2: Factorize the quadratic term
The quadratic term in the expression is -2r square. To factorize this term, we can use the difference of squares formula, which states that a square minus b square can be factored as (a+b)(a-b).

In our case, a is -2r and b is 0. Applying the difference of squares formula, we have:
-2r square = (-2r + 0)(-2r - 0)
= (-2r)(-2r)
= 4r square

The expression now becomes 84-2r-4r square.

Step 3: Factorize the remaining terms
Now, we need to factorize the remaining terms: 84-2r. To do this, we can look for common factors between the two terms.

In this case, there are no common factors between 84 and -2r. Therefore, we move on to the next step.

Step 4: Factorize by grouping
Since we couldn't find any common factors, we can try factoring by grouping. We group the terms together in pairs and factor out the common factors from each pair.

Grouping the terms, we have:
(84-2r-4r square) = (84-2r) - (4r square)

Now, let's factor out the common factors from each group separately.

From the first group (84-2r), the common factor is 2:
= 2(42-r)

From the second group (4r square), the common factor is 4r square itself.

So, the expression can be written as:
= 2(42-r) - 4r square

Step 5: Simplify the expression
To simplify the expression further, we can combine the terms within the parentheses:
= 2(42-r) - 4r square

Therefore, the factorized form of the expression 84-2r-2r square is:
2(42-r) - 4r square

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