Educational

Factorize x(x³ – y³) + 3xy(x – y) Question: Factorize: \[ x(x^3-y^3)+3xy(x-y) \] Solution: \[ x(x^3-y^3)+3xy(x-y) \] \[ =x(x-y)(x^2+xy+y^2)+3xy(x-y) \] \[ =(x-y)\left[x(x^2+xy+y^2)+3xy\right] \] \[ =(x-y)(x^3+x^2y+xy^2+3xy) \] \[ =(x-y)\left(x^3+x^2y+xy^2+y^3-y^3+3xy\right) \] \[ =(x-y)\left[(x+y)(x^2+y^2)+xy(x+y)-y^3+3xy\right] \] \[ =(x-y)(x+y)(x^2+y^2+xy) \] \[ \boxed{(x-y)(x+y)(x^2+xy+y^2)} \] Next Question / Full Exercise

Factorize a²x² + (ax² + 1)x + a Question: Factorize: \[ a^2x^2+(ax^2+1)x+a \] Solution: \[ a^2x^2+(ax^2+1)x+a \] \[ =a^2x^2+ax^3+x+a \] \[ =ax(ax+x^2)+1(x+a) \] \[ =ax(x+a)+1(x+a) \] \[ =(x+a)(ax+1) \] \[ \boxed{(x+a)(ax+1)} \] Next Question / Full Exercise

Factorize a(a + b)³ – 3a²b(a + b) Question: Factorize: \[ a(a+b)^3-3a^2b(a+b) \] Solution: \[ a(a+b)^3-3a^2b(a+b) \] \[ =a(a+b)\left[(a+b)^2-3ab\right] \] \[ =a(a+b)\left[a^2+2ab+b^2-3ab\right] \] \[ =a(a+b)(a^2-ab+b^2) \] \[ \boxed{a(a+b)(a^2-ab+b^2)} \] Next Question / Full Exercise

Factorize a(a + b)³ – 3a²b(a + b) Question: Factorize: \[ a(a+b)^3-3a^2b(a+b) \] Solution: \[ a(a+b)^3-3a^2b(a+b) \] \[ =a(a+b)\left[(a+b)^2-3ab\right] \] \[ =a(a+b)\left[a^2+2ab+b^2-3ab\right] \] \[ =a(a+b)(a^2-ab+b^2) \] \[ \boxed{a(a+b)(a^2-ab+b^2)} \] Next Question / Full Exercise

Factorize x³ + x – 3x² – 3 Question: Factorize: \[ x^3+x-3x^2-3 \] Solution: \[ x^3+x-3x^2-3 \] \[ =x^3-3x^2+x-3 \] \[ =x^2(x-3)+1(x-3) \] \[ =(x-3)(x^2+1) \] \[ \boxed{(x-3)(x^2+1)} \] Next Question / Full Exercise

Assertion and Reason Questions on Algebraic Identities Question: Each of the following questions contains STATEMENT-1 (Assertion) and STATEMENT-2 (Reason) and has following four choices (a), (b), (c) and (d), only one of which is the correct answer. (a) Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1. (b) Statement-1 is true,

Assertion and Reason Questions on Algebraic Identities Question: Each of the following questions contains STATEMENT-1 (Assertion) and STATEMENT-2 (Reason) and has following four choices (a), (b), (c) and (d), only one of which is the correct answer. (a) Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1. (b) Statement-1 is true,

Assertion and Reason Questions on Algebraic Identities Question: Each of the following questions contains STATEMENT-1 (Assertion) and STATEMENT-2 (Reason) and has following four choices (a), (b), (c) and (d), only one of which is the correct answer. (a) Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1. (b) Statement-1 is true,

Assertion and Reason Questions on Algebraic Identities Question: Each of the following questions contains STATEMENT-1 (Assertion) and STATEMENT-2 (Reason) and has following four choices (a), (b), (c) and (d), only one of which is the correct answer. (a) Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1. (b) Statement-1 is true,

Assertion and Reason Questions on Algebraic Identities Question: Each of the following questions contains STATEMENT-1 (Assertion) and STATEMENT-2 (Reason) and has following four choices (a), (b), (c) and (d), only one of which is the correct answer. (a) Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1. (b) Statement-1 is true,