Question

write all 13 algebric identities with proof​

Answer 1

Answer:

(a + b)2 = a2 + 2ab + b. ...

(a – b)2 = a2 – 2ab + b. ...

a2 – b2 = (a + b)(a – b)

(x + a)(x + b) = x2 + (a + b) x + ab.

(a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca.

(a + b)3 = a3 + b3 + 3ab (a + b)

(a – b)3 = a3 – b3 – 3ab (a – b)

a3 + b3 + c3– 3abc = (a + b + c)(a2 + b2 + c2 – ab – bc – ca)

Step-by-step explanation:

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Answer 2

Answer:

$1. (a + b)^2 = a^2 + 2ab + b^ 2\\2. (a - b)^2 = a^2 - 2ab + b^2\\3. (a+b)(a-b) = a^2 - b^2\\4.(a+b+c)^2= a^2 + b^2 +c^2 + 2ab+2bc+2ca\\5. (a+b)^3 = a^3 + b^3 + 3ab(a+b)\\6.(a-b)^3= a^3 -b^3 - 3ab(a-b)\\7. a^3+b^3 = (a+b) (a^2 - ab + b^2)\\8. a^3 - b^3 = (a-b) (a^2 +ab + b^2)\\9. (x+a)(x+b) = x^2 + (a+b) x + ab\\10.a^3 +b^3+c^3-3abc = (a+b+c)(a^2 + b^2 + c^2-ab-bc-ca)\\11. if a+b+c=0 ; then-> a^3+b^3+c^3= 3abc$