Factorise $a^4 - b^2$ . Answer ... Factorise completely $8xy - 1 - 4x + 2y$ . Answer ...

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Worked solution

1. Apply the difference of squares identity

$a^4-b^2=(a^2)^2-b^2$

Using $x^2-y^2=(x+y)(x-y)$ ,

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

Answer

$(a^2+b)(a^2-b)$

1. Group terms to obtain a common binomial factor

$8xy - 1 - 4x + 2y$

$= 8xy - 4x + 2y - 1$

$= 4x(2y-1) + 1(2y-1)$

2. Factorise the common binomial factor completely

$4x(2y-1) + 1(2y-1)$

$= (2y-1)(4x+1)$

Answer

$(2y-1)(4x+1)$

AI analysis — may contain mistakes.

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