Question

factorise 4x^2-4a^2+(a^4-b^4)

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Answer 1

Answer:

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