If 5x² − 8y − 20x + 2xy = (x + a) (bx + 2y), then the value of (a − b) is :

The correct option is −9.

We are given the algebraic identity:

$5x^2-8y-20x+2xy=(x+a)(bx+2y)$

First, let us factorize the expression on the left-hand side by grouping terms appropriately.

Rearranging the terms on the left side:

$5x^2-20x+2xy-8y$

Group the first two terms together and the last two terms together:

$(5x^2-20x)+(2xy-8y)$

Factor out the common terms from each group:

$5x(x-4)+2y(x-4)$

Now, factor out the common binomial factor $(x-4)$:

$(x-4)(5x+2y)$

Now, compare this factorized expression with the right-hand side of the given equation, $(x+a)(bx+2y)$:

$(x-4)(5x+2y)=(x+a)(bx+2y)$

Equating the corresponding components from both sides, we get:

$a=-4$

$b=5$

We are asked to find the value of $(a-b)$:

$a-b=-4-5=-9$

Thus, the value of $(a-b)$ is −9.