Here are the identities that you need to learn and remember. You could revise some of the identities from our notes for students of Class 8. Click Here.

Definition: Identity is an equality which is true for all values of the variables.

Some the identities are given below that you will have to familiarise yourself for solving problems.

Identities for a binomial:

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

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

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

Identities for square of a trinomial:

${(a+b+c)}^2=\left(a^2+b^2+c^2\right)+2(ab+bc+ca)$

${(a+b-c)}^2=\left(a^2+b^2+c^2\right)+2(ab-bc-ca)$

${(a-b+c)}^2=\left(a^2+b^2+c^2\right)+2(-ab-bc+ca)$

${(-a+b+c)}^2=\left(a^2+b^2+c^2\right)+2(-ab+bc-ca)$

${(a-b-c)}^2=\left(a^2+b^2+c^2\right)+2(-ab+bc-ca)$

Identities for cube of a binomial:

${(a+b)}^3=\ a^3+b^3+3ab(a+b)$

${(a-b)}^3=\ a^3-b^3-3ab(a-b)$

${a^3+b^3=\ (a+b)}^3-3ab(a+b)$

${a^3-b^3=\ (a-b)}^3+3ab(a-b)$

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

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

Identities for cube of a trinomial:

$a^3+b^3+c^3 -3abc = (a+b+c)(a^2+b^2+c^2-ab-bc-ca)$

$(a+b+c)^3 = a^3+b^3+c^3 +3ab(b+a)+3bc(b+c) + 3ca(c+a) + 6abc$

Some other identities:

$(x+a)(x+b) = x^2 + (a+b)x+ab$

$(x+a)(x-b) = x^2 + (a-b)x-ab$

$(x-a)(x+b) = x^2 - (a-b)x-ab$

$(x-a)(x-b) = x^2 - (a+b)x+ab$

$(x+a)(x+b)(x+c) = x^3+x^2(a+b+c) +x(ab+bc+ca)+abc$