Question

${(a + b)}^{2} - ( {b - a)}^{2 } \\ factorise$
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Answer 1

$( {a + b)}^{2} - ( {b - a)}^{2} \\ \\ = (a + b + b - a)(a + b - b + a) \\ \\ = 2b.2a \\ \\ = 4ab$

Answer 2

Answer:

$(a + b) ^{2} - (b - a) ^{2} \\ \\ = a ^{2} + 2ab + {b}^{2} - ( {b}^{2} - 2ab + {a}^{2} ) \\ \\ = {a}^{2} + 2ab + {b}^{2} - {b}^{2} + 2ab - {a}^{2} \\ \\ = 2ab + 2ab \\ \\ = 4ab \\ \\ ( + {a}^{2} \: and \: - {a}^{2} \: cancelled) \\ \\ (similarly \: + {b}^{2} \: and \: { - b}^{2} \: cancelled) \\ \\ formula \: used \\ \\ (a + b) ^{2} = {a}^{2} + 2ab + {b}^{2} \\ \\ and \\ \\ (a - b) ^{2} = {a}^{2} - 2ab + {b}^{2}$

hope it helps uH :)