Question

solve the factorisation

Answer 1

${a}^{2} + {b}^{2} + 2ab - 8a + 8b + 12$
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Answer 2

Answer -

$1. \: ( {a - b)}^{2} - 8(a - b) + 12 \\ \\ write \: - 8(a - b) \: as \: a \: difference \\ \\ ( {a - b)}^{2} - 2(a - b) - 6(a - b) + 12 \\ \\ factor \: out \: \: a - b \: \: from \: the \: expression \\ \\ (a - b)(a - b - 2) - 6 (a - b) + 12 \\ \\ factor \: out \: - 6 \: from \: the \: expression \\ \\ (a - b)(a - b - 2) - 6(a - b - 2) \\ \\ factor \: out \: a - b - 2 \: from \: the \: expression \\ \\ (a - b - 2)(a - b - 6)$


$2. \: \: 3(m { + 2n)}^{2} - 2(m + 2n) - 16 \\ \\ write \: - 2(m + 2n) \: \: as \: a \: difference \\ \\ 3(m + 2n {)}^{2} + 6(m + 2n) - 8(m + 2n) - 16 \\ \\ factor \: out \: 3(m + 2n) \: and \: - 8 \\ from \: the \: expression \\ \\ 3(m + 2n)(m + 2n + 2) - 8(m + 2n + 2) \\ \\ factor \: out \: m + 2n + 2 \: from \: the \: expression \\ \\ (m + 2n + 2)(3(m + 2n) - 8) \\ \\ (m + 2n + 2)( 3m + 6n - 8)$

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