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

Dimensions of a Cuboid Having Volume 3x² – 12x What are the possible expressions for the dimensions of the cuboid whose volume is : \(3x^2 – 12x\) \[ 3x^2 – 12x \] \[ = 3x(x – 4) \] \[ = 3 \times x \times (x – 4) \] \[ \therefore \] \[ \text{Possible dimensions are

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