Math, asked by pathak0404, 11 months ago

Factorise: a^3 - b^3 + 1 + 3abc​

Answers

Answered by satnalikaanjali
0

(a+b-1)(a^2+b^2-ab+a+b+1)

Answered by TRISHNADEVI
3

 \huge{ \underline{ \overline{ \mid{ \mathfrak{ \purple{ \:   \: SOLUTION \:  \: } \mid}}}}}

TO FACTORISE :-

 \huge{ \sf{ \pink{a {}^{3} -  b {}^{3} + 1 +  3ab}}}

 \:  \:  \:  \:  \:  \: \tt{ \red{a {}^{3} -  b {}^{3} + 1 +  3ab }}\\  \\    \tt{ \blue{= (a) {}^{3} + ( - b) {}^{3} + (1) {}^{3}   - 3 \times a \times ( - b) \times 1 }}\\  \\  \tt{ \green{ =  \{a  +  ( - b )+ 1 \} \{ (a) {}^{2} + ( -  b) {}^{2} +( 1) {}^{2}   - a \times ( - b) - }} \\\tt{ \green{\:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \: (-  b) \times 1 - 1 \times a \}}} \\  \\   \tt{ \blue{= (a - b + 1)(a {}^{2}  +  b {}^{2} + 1 +  ab + b - a)}} \\  \\  \tt{ \red{= (a - b + 1)(a {}^{2}  +  b {}^{2} + 1  - a + b+  ab)}}

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