Question

factorize: (a^2-b^2)(c^2-d^2)-4abcd​

Answer 1

Step-by-step explanation:

$( {a}^{2} - {b}^{2} )( {c}^{2} - {d}^{2} ) - 4abcd$

Opening brackets we get

${a}^{2} {c}^{2} - {a}^{2} {d}^{2} - {b}^{2} {c}^{2} + {b}^{2} {d}^{2} - 4abcd$

Now Using 4abdcd=2abcd+2abcd we get

$(( {ac)}^{2} + ({bd)}^{2} - 2abcd) - ( ({ad)}^{2} + {(bc)}^{2} + 2abcd)$

using Identity

$( {a + b)}^{2} = {a}^{2} + {b}^{2} + 2ab$

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

we get

${(ac - bd)}^{2} ( {ad + bc)}^{2}$