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 the following expression : a^2x^2 + (ax^2 + 1)x + a Read More »
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 the following expression : a(a + b)^3 – 3a^2b(a + b) Read More »
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
Factorize the following expression : x^3 + x – 3x^2 -3 Read More »
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,
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,
If 2x + y/3 = 12 and xy = 30, then 8x³ + y³/27 = Question: If \[ 2x+\frac{y}{3}=12 \] and \[ xy=30, \] then \[ 8x^3+\frac{y^3}{27}= \] (a) 1008 (b) 168 (c) 106 (d) none of these Solution: \[ \left(2x+\frac{y}{3}\right)^3 = (2x)^3+\left(\frac{y}{3}\right)^3 +3(2x)\left(\frac{y}{3}\right)\left(2x+\frac{y}{3}\right) \] \[ 12^3 = 8x^3+\frac{y^3}{27} +3(2x)\left(\frac{y}{3}\right)(12) \] \[ 1728 = 8x^3+\frac{y^3}{27}
If 2x + y/3 = 12 and xy = 30, then 8x^3 + y^3/27 = Read More »