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Standard VI

Mathematics

Variable

Question 8Sum...

Question

Question 8

Sum of $a - b + a b, b + c - b c$ and $c - a - a c$ is
a) $2 c + a b - a c - b c$
b) $2 c - a b - a c - b c$
c) $2 c + a b + a c + b c$
d) $2 c - a b + a c + b c$

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Solution

a) $2 c + a b - a c - b c$

$\to$ Required sum = $(a - b + a b) + (b + c - b c) + (c - a - a c) = a - b + a b + b + c - b c + c - a - a c [a d d i n g t h e l i k e t e r m s a n d r e t a i n i n g o t h e r s] = 2 c + a b - a c - b c$

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Similar questions

Prove that $∣ ∣ ∣ ∣ ∣ \begin{matrix} a^{2} & b c & a c + c^{2} a^{2} + a b & b^{2} & a c a b & b^{2} + b c & c^{2} \end{matrix} ∣ ∣ ∣ ∣ ∣ = 4 a^{2} b^{2} c^{2}$

Q. Let

A = a^{2} b + a b^{2} - a^{2} c - a c^{2},

B = b^{2} c + b c^{2} - a^{2} b - a b^{2}

and

C = a^{2} c + a c^{2} - b^{2} c - b c^{2}

, where

a > b > c > 0

. If the equation

A x^{2} + B x + C = 0

has equal roots, then

a, b, c

are in

In Δ ABC if ∠A = ∠B, then

Q. Factorise

a^{2} b + a^{2} c + a b^{2} + b^{2} c + a c^{2} + b c^{2} + 3 a b c

In $Δ$ ABC, right angled at B, expressions for sec C and cosec C is

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Variable

Standard VI Mathematics

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Question 8 Sum of a−b+ab, b+c−bc and c−a−ac is a) 2c+ab−ac−bc b) 2c−ab−ac−bc c) 2c+ab+ac+bc d) 2c−ab+ac+bc

a) 2c+ab−ac−bc →​​​​​​​Required sum = (a−b+ab)+(b+c−bc)+(c−a−ac)=a−b+ab+b+c−bc+c−a−ac [adding the like terms and retaining others]=2c+ab−ac−bc

Question 8

Sum of $a - b + a b, b + c - b c$ and $c - a - a c$ is
a) $2 c + a b - a c - b c$
b) $2 c - a b - a c - b c$
c) $2 c + a b + a c + b c$
d) $2 c - a b + a c + b c$

a) $2 c + a b - a c - b c$

$\to$ Required sum = $(a - b + a b) + (b + c - b c) + (c - a - a c) = a - b + a b + b + c - b c + c - a - a c [a d d i n g t h e l i k e t e r m s a n d r e t a i n i n g o t h e r s] = 2 c + a b - a c - b c$