Question
Factorise the following by the difference of two squares:$16a^4 - 81b^4$
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Answer
$16a^4 - 81b^4$
$= (4a^2)^2 - (9b^2)^2$
$= (4a^2 - 9b^2)(4a^2 + 9b^2)$
$= [(2a)^2 - (3b)^2](4a^2 + 9b^2)$
$= [(2a - 3b)(2a + 3b)](4a^2+ 9b^2)$
$= (2a - 3b)(2a + 3b)(4a^2 + 9b^2).$
$= (4a^2)^2 - (9b^2)^2$
$= (4a^2 - 9b^2)(4a^2 + 9b^2)$
$= [(2a)^2 - (3b)^2](4a^2 + 9b^2)$
$= [(2a - 3b)(2a + 3b)](4a^2+ 9b^2)$
$= (2a - 3b)(2a + 3b)(4a^2 + 9b^2).$
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