Verify the following: (ab + bc)(ab - bc) + (bc + ca)(bc - ca) + (… - Vidyadip

Question

Verify the following: $(ab + bc)(ab - bc) + (bc + ca)(bc - ca) + (ca + ab)(ca - ab) = 0$

✓

Answer

$(ab + bc)(ab - bc) + (bc + ca)(bc - ca) + (ca + ab)(ca - ab) = 0$
Taking $LHS$
$(ab + bc)(ab - bc) + (bc + ca)(bc - ca) + (ca + ab)(ca - ab)$
$ =\left[(a b)^2-(b c)^2\right]+\left[(b c)^2-(c a)^2\right]+\left[(c a)^2-(a b)^2\right] $
$=a^2 b^2-b^2 c^2+b^2 c^2-c^2 a^2+c^2 a^2-a^2 b^2=0 $
$= RHS$
Hence verified

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "3 Marks Question" from Algebraic Expressions, Identities and Factorisation→Algebraic Expressions, Identities and Factorisation — all question types→MATHS STD 8 question papers→Gujarat Board STD 8 question papers→Gujarat Board question paper generator→

Similar questions

Living on your own: Sanjay is looking for one-bedroom appartment on rent. At Neelgiri appartments, rent for the first two months is $20 \%$ off. The one bedroom rate at Neelgiri is Rs. $6,000$ per month. At Savana appartments, the first month is $50 \%$ off. The one bedroom rate at Savana appartments is Rs. $7000$ per month. Which appartment will be cheaper for the first two months? By how much?

Find a positive value of x for which the given equation is satisfied.
$\frac{\text{x}^2-9}{5+\text{x}^2}=\frac{-5}{9}$

By what per cent is ₹ $2000$ less than ₹ $2400?$ Is it the same as the per cent by which ₹ 2400 is more than ₹ 2000?

Draw the line graph using suitable scale to show the annual gross profit of a company for a period of five years.

Years	$1$st	$2$nd	$3$rd	$4$th	$5$th
Gross profit (in ₹)	$1700000$	$1550000$	$1140000$	$1210000$	$1490000$

If $56x32y$ is divisible by $18$, find the least value of $y.$

The circumference of the base of a cylinder is $88\ cm$ and its height is $15\ cm.$ Find the volume of the cylinder.

The area of a square plot is $101\frac{1}{400}\text{m}^2.$ Find the length of one side of the plot.

Find the length of the diagonal of a rectangle whose sides are $12\ cm$ and $5\ cm.$

The sum of three consecutive odd natural numbers is $69$. Find the prime number out of these numbers.

$10$ people can dig a trench in $6$ days. How many people can dig it in $4$ days?