Answer:

To factorize the expression 5-4(a-b) -12(a-b)², we can start by factoring out the common factor (a-b). Let's break it down step by step:

First, let's factor out (a-b) from the expression:

(a-b)(-4 - 12(a-b))

Now, let's simplify further:

(a-b)(-4 - 12a + 12b)

And that's the factored form of the expression!

Step-by-step explanation:

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Verified answer

Answer:

[tex]\boxed{\bf\:5 - 4(a - b) - 12 {(a - b)}^{2} = \left[ 6a - 6b + 5\right]\left[ (1 - 2a + 2b\right] \: } \\ [/tex]

Step-by-step explanation:

Given algebraic expression is

[tex] \sf \: 5 - 4(a - b) - 12 {(a - b)}^{2} \\ [/tex]

Let assume that a - b = k

So, above expression can be rewritten as

[tex] \sf \: = \: 5 - 4k - {12k}^{2} \\ [/tex]

[tex] \sf \: = \: - \left[ {12k}^{2} + 4k - 5\right] \\ [/tex]

On splitting the middle terms, we get

[tex] \sf \: = \: - \left[ {12k}^{2} + 10k - 6k - 5\right] \\ [/tex]

[tex] \sf \: = \: - \left[ 2k(6k + 5) - (6k + 5)\right] \\ [/tex]

[tex] \sf \: = \: - \left[(6k + 5)(2k - 1)\right] \\ [/tex]

[tex] \sf \: = \: (6k + 5)(1 - 2k) \\ [/tex]

On substituting the value of k, we get

[tex] \sf \: = \: \left[ 6(a - b) + 5\right]\left[ (1 - 2(a - b)\right]\\ [/tex]

[tex] \sf \: = \: \left[ 6a - 6b + 5\right]\left[ (1 - 2a + 2b\right]\\ [/tex]

Hence,

[tex]\boxed{\bf\:5 - 4(a - b) - 12 {(a - b)}^{2} = \left[ 6a - 6b + 5\right]\left[ (1 - 2a + 2b\right] \: } \\ [/tex]

[tex]\rule{190pt}{2pt}[/tex]

We assume the other variable such as k, to make the calculations easier.