Question

(2a-b)²+2(2a-b)-8 find. its answer please

Answer 1

Answer:

Factorisation of (2a-b)²+2(2a-b)-8

= (2a-b+4)(2a-b-2)

Explanation:

Given (2a-b)²+2(2a-b)-8

To Find:

Factorisation of (2a-b)²+2(2a-b)-8

solution:

Splitting the middle term, we get

= (2a-b)²+4(2a-b)-2(2a-b)-8

= (2a-b)[2a-b+4]-2[2a-b+4]

= (2a-b+4)(2a-b-2)

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Answer 2

The value of $\bold{(2 a-b)^{2}+2(2 a-b)-8\ is\ 4 a^{2} - 4ab+4 a+b^{2}-2 b-8}$

Solution:  

To find the value of the above question, let us simplify it first;

The question $(2 a-b)^{2}+2(2 a-b)-8$  can be written as $x^{2}+2 x-8$

Therefore we can take 2a-b = x, we get

Now we solve the equation $x^{2}+2 x-8$, by forming the roots of x, we get

$\begin{array}{l}={x^{2}+4 x-2 x-8} \\ \\={x(x+4)-2(x+4)} \\ \\={(x-2)(x+4)}\end{array}$

The value of x = 2, -4. Putting the value we get 2a-b = x, which is either 2a-b = 2 or 2a-b = -4.

Now to multiplying (2a – b – 2) and (2a – b + 4) we get  

(2a – b – 2).(2a – b + 4) =  $\bold{4 a^{2}-4 a b+4 a+b^{2}-2 b-8}$