Length and Breadth of Rectangle Having Area 35y² + 13y – 12 Give possible expressions for the length and breadth of rectangle having area : \(35y^2 + 13y – 12\) \[ 35y^2 + 13y – 12 \] \[ = 35y^2 + 28y – 15y – 12 \] \[ = 7y(5y + 4) – 3(5y + […]

Factorize the Expression (a – b + c)² + (b – c + a)² + 2(a – b + c)(b – c + a) Factorize the following expression : \((a – b + c)^2 + (b – c + a)^2 + 2(a – b + c)(b – c + a)\) \[ (a – b +

Factorize the Expression x² + 12/35x + 1/35 Factorize the following expression : \(x^2 + \frac{12}{35}x + \frac{1}{35}\) \[ x^2 + \frac{12}{35}x + \frac{1}{35} \] \[ = x^2 + \frac{5}{35}x + \frac{7}{35}x + \frac{1}{35} \] \[ = x\left(x + \frac{1}{7}\right) + \frac{1}{5}\left(x + \frac{1}{7}\right) \] \[ = \left(x + \frac{1}{7}\right)\left(x + \frac{1}{5}\right) \] Next Question

Factorize the Expression 2x² – 5/6x + 1/12 Factorize the following expression : \(2x^2 – \frac{5}{6}x + \frac{1}{12}\) \[ 2x^2 – \frac{5}{6}x + \frac{1}{12} \] \[ = 2x^2 – \frac{1}{2}x – \frac{1}{3}x + \frac{1}{12} \] \[ = x\left(2x – \frac{1}{2}\right) – \frac{1}{6}\left(2x – \frac{1}{2}\right) \] \[ = \left(2x – \frac{1}{2}\right)\left(x – \frac{1}{6}\right) \] Next Question

Factorize the Expression x(x³ – y³) + 3xy(x – y) Factorize the following expression : \(x(x^3 – y^3) + 3xy(x – y)\) \[ x(x^3 – y^3) + 3xy(x – y) \] \[ = x(x – y)(x^2 + xy + y^2) + 3xy(x – y) \] \[ = (x – y)\left[x(x^2 + xy + y^2) +

Factorize the Expression x² – y² – 4xz + 4z² Factorize the following expression : \(x^2 – y^2 – 4xz + 4z^2\) \[ x^2 – y^2 – 4xz + 4z^2 \] \[ = (x^2 – 4xz + 4z^2) – y^2 \] \[ = (x – 2z)^2 – y^2 \] \[ = (x – 2z –

Factorize the Expression a² + 4b² – 4ab – 4c² Factorize the following expression : \(a^2 + 4b^2 – 4ab – 4c^2\) \[ a^2 + 4b^2 – 4ab – 4c^2 \] \[ = (a^2 – 4ab + 4b^2) – 4c^2 \] \[ = (a – 2b)^2 – (2c)^2 \] \[ = (a – 2b –

Factorize a² + 2ab + b² – c² Question: Factorize: \[ a^2+2ab+b^2-c^2 \] Solution: \[ a^2+2ab+b^2-c^2 \] \[ =(a+b)^2-c^2 \] \[ =(a+b-c)(a+b+c) \] \[ \boxed{(a+b-c)(a+b+c)} \] Next Question / Full Exercise

Factorize 21x² – 2x + 1/21 Question: Factorize: \[ 21x^2-2x+\frac{1}{21} \] Solution: \[ 21x^2-2x+\frac{1}{21} \] \[ =21x^2-2\left(x\cdot\frac{1}{21}\right)+\frac{1}{21^2}\cdot21 \] \[ =21\left(x^2-\frac{2x}{21}+\frac{1}{441}\right) \] \[ =21\left(x-\frac{1}{21}\right)^2 \] \[ =\left(\sqrt{21}x-\frac{1}{\sqrt{21}}\right)^2 \] \[ \boxed{21\left(x-\frac{1}{21}\right)^2} \] Next Question / Full Exercise

Factorize x(x – 2)(x – 4) + 4x – 8 Question: Factorize: \[ x(x-2)(x-4)+4x-8 \] Solution: \[ x(x-2)(x-4)+4x-8 \] \[ =x(x-2)(x-4)+4(x-2) \] \[ =(x-2)\{x(x-4)+4\} \] \[ =(x-2)(x^2-4x+4) \] \[ =(x-2)(x-2)^2 \] \[ =(x-2)^3 \] \[ \boxed{(x-2)^3} \] Next Question / Full Exercise