Advertisements
Advertisements
प्रश्न
Show that: (a − b)(a + b) + (b − c)(b + c) + (c − a)( c + a) = 0
Advertisements
उत्तर
\[\text { LHS } = \left( a - b \right)\left( a + b \right) + \left( b - c \right)\left( b + c \right) + \left( c + a \right)\left( c - a \right)\]
\[ = a^2 - b^2 + b^2 - c^2 + c^2 - a^2 \left[ \because \left( a + b \right)\left( a - b \right) = a^2 - b^2 \right]\]
\[ = a^2 - b^2 + b^2 - c^2 + c^2 - a^2 \]
\[ = 0\]
= RHS
Because LHS is equal to RHS, the given equation is verified.
संबंधित प्रश्न
Find each of the following product:
\[\left( - \frac{2}{7} a^4 \right) \times \left( - \frac{3}{4} a^2 b \right) \times \left( - \frac{14}{5} b^2 \right)\]
Find each of the following product: \[\left( \frac{4}{3}p q^2 \right) \times \left( - \frac{1}{4} p^2 r \right) \times \left( 16 p^2 q^2 r^2 \right)\]
Find the following product: \[\frac{6x}{5}( x^3 + y^3 )\]
Simplify: x3y(x2 − 2x) + 2xy(x3 − x4)
Simplify: a(b − c) − b(c − a) − c(a − b)
Multiply:
(x2 + y2) by (3a + 2b)
Multiply: \[\left( - \frac{a}{7} + \frac{a^2}{9} \right)by\left( \frac{b}{2} - \frac{b^2}{3} \right)\].
Simplify:
(5x − 3)(x + 2) − (2x + 5)(4x − 3)
Simplify:
(3x + 2y)(4x + 3y) − (2x − y)(7x − 3y)
Simplify : (m2 − n2m)2 + 2m3n2
