Question

(v) x2 - 1 - 2y - y
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Answer 1

Step-by-step explanation:

Rearrange the terms as follows:

x^2 — y^2 — 2y — 1

Group the last three terms, factoring out a —1:

x^2 — (y^2 + 2y + 1)

Those last three terms are a perfect square:

x^2 — (y + 1)^2

Now you have the difference of two squares:

[x — (y + 1)][x + (y + 1)]

Remove the inner grouping symbols to get

(x — y — 1)(x + y + 1)

Answer 2

Step-by-step explanation:

To solve

x2 - 1 - 2y - y

Solution

Rearrange the given terms as follows:

$\rm \orange{ {x}^{2} - {y}^{2} - 2y - 1}$

Group the last three terms , factoring out a - 1:

$\rm \pink{{x}^{2} - ( {y}^{2} + 2y + 1)}$

Those last three terms are a perfect square:

$\rm \green{ {x}^{2} - {(y + 1)}^{2} }$

Now, we will take out the difference of the two squares:

$\rm \blue{[x - (y - 1)][x + (y + 1)]}$

Remove the inner two grouping symbols to get:

$\rm \red{(x - y - 1)(x + y + 1)}$

• U can also use the formula (a²+b²) = (a+b) (a-b)