Question

simplify (a + b) (a^2+ b^2 -2 a b)- (a-b) (a^2 + b^2+ 2 AB)

Answer 1

$\underline{\large\bf{\mathfrak{Hello!}}}$

$= > (a + b)( {a}^{2} + {b}^{2} - 2ab) - (a - b)( {a}^{2} + {b}^{2} + 2ab) \\ \\ = > (a + b) {(a - b)}^{2} - (a - b) {(a + b)}^{2} \\ \\ = > (a - b)[(a + b)(a - b) - (a + b)(a + b)] \\ \\ = > (a - b)(a + b)[(a - b) - (a + b)] \\ \\ = > ({a}^{2} - {b}^{2} )[a - b - a - b] \\ \\ = > ({a}^{2} - {b}^{2}) ( - 2b) \\ \\ = > - 2 {a}^{2} b + 2 {b}^{3} \\ \\ = > 2 {b}^{3} - 2 {a}^{2} b$

$\boxed{2 {b}^{3} - 2 {a}^{2} b }$

$\bf{\mathfrak{Hope \: this \: helps...:)}}$

Answer 2

♣ Qᴜᴇꜱᴛɪᴏɴ :

$\left(a\:+\:b\right)\:\left(a^2+\:b^2\:-2\:a\:b\right)-\:\left(a-b\right)\:\left(a^2\:+\:b^2+\:2ab\right)$

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♣ ᴀɴꜱᴡᴇʀ :

$\left(a+b\right)\left(a^2+b^2-2ab\right)-\left(a-b\right)\left(a^2+b^2+2ab\right)=-2a^2b+2b^3$

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♣ ᴄᴀʟᴄᴜʟᴀᴛɪᴏɴꜱ :

$\left(a+b\right)\left(a^2+b^2-2ab\right)-\left(a-b\right)\left(a^2+b^2+2ab\right)$

$=a^3-a^2b-ab^2+b^3-\left(a-b\right)\left(a^2+b^2+2ab\right)$

$=a^3-a^2b-ab^2+b^3-a^3-a^2b+ab^2+b^3$

$=-2a^2b+2b^3$