Question

(x-2y)whole square-5(x-2y)+6

Answer 1

Hey there!

Given, expand the following equation, $\bf{(x - 2y)^2 - 5 (x - 2y) + 6}$

By applying the law of distribution that is, a (b - c)= ab - ac.

Here, a = - 5 , b = x and c = 2y.

$\bf{(x - 2y)^2 - 5x - (- 5) \times 2y}$

$\bf{(x - 2y)^2 - 5x + 10y + 6}$

Applying the law of perfect square formula that is,

$\bf{(a - b)^2 = a^2 - 2 ab + b^2}$.

Now, here, a = x and b = 2y.

$\bf{x^2 - 2x \times 2y + (2y)^2 - 5x +10y + 6}$

Multiply the numbers and add the exponential rule, subsequently to complete the squaring of this equation.

Final answer :

$\boxed{\bf{x^2 - 4xy + 4y^2 - 5x + 10y + 6}}$

Which is the required solution for this type of query.

If Factorization was asked then here's the solution :

Break the expression given in the question into groups;

$\bf{((x - 2y)^2 - 2(x - 2y)) + (- 3(x - 2y) + 6)}$

Factoring out the common term (x - 2y) from $\bf{(x - 2y)^2 - 2(x - 2y)}$.

And, factoring out the term or value of "- 3" from the equation - 3 (x - 2y) + 6.

= (x - 2y) ( (x - 2y) - 2) - 3 ( (x - 2y) -2)

Factor out the common term of ( (x - 2y) - 2):

= ( (x - 2y) - 2) ( (x - 2y) - 3)

Refine the terms to obtain a final value:

$\boxed{\bf{Answer \: = (x - 2y - 2) \: (x - 2y - 3)}}$

Which is the second required solution for this type of query.

Hope this helps you and solves your doubts for this!