Question

Factorise: 25x² − 1 − 2y − y²
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Answer 1

Rearrange the terms as follows:

Rearrange the terms as follows:x^2 — y^2 — 2y — 1

Rearrange the terms as follows:x^2 — y^2 — 2y — 1Group the last three terms, factoring out a —1:

Rearrange the terms as follows:x^2 — y^2 — 2y — 1Group the last three terms, factoring out a —1:x^2 — (y^2 + 2y + 1)

Rearrange the terms as follows:x^2 — y^2 — 2y — 1Group the last three terms, factoring out a —1:x^2 — (y^2 + 2y + 1)Those last three terms are a perfect square:

Rearrange the terms as follows:x^2 — y^2 — 2y — 1Group 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

Rearrange the terms as follows:x^2 — y^2 — 2y — 1Group 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)^2Now you have the difference of two squares:

Rearrange the terms as follows:x^2 — y^2 — 2y — 1Group 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)^2Now you have the difference of two squares:[x — (y + 1)][x + (y + 1)]

Rearrange the terms as follows:x^2 — y^2 — 2y — 1Group 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)^2Now you have the difference of two squares:[x — (y + 1)][x + (y + 1)]Remove the inner grouping symbols to get

Rearrange the terms as follows:x^2 — y^2 — 2y — 1Group 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)^2Now 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)

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