Find the following products: (2a - 3b - 2c)(4a^2 + 9b^2 + 4c^2 + … - Vidyadip

Question

Find the following products: $(2a - 3b - 2c)(4a^2 + 9b^2 + 4c^2 + 6ab - 6bc + 4ca)$

✓

Answer

We have, $(2 a-3 b-2 c)\left(4 a^2+9 b^2+4 c^2+6 a b-6 b c+4 c a\right) $
$=(2 a+(-3 b)+(-2 c))+\left((2 a)^2+(-3 b)^2+(-2 c)^2-(2 a)(-3 b)(-2 c)-(-2 c)(2 a)\right)$
$=(2 a)^3+(-3 b)^3+(-2 c)^3-3(2 a)(-3 b)(-2 c)\left[\because a^3+b^3+c^3-3 a b c=(a+b+c)\left(a^2+b^2+c^2-a b-b c-c a\right)\right]$
$=8 a^3-27 b^3-8 c^3-36 a b c$
$\therefore(2 a-3 b-2 c)\left(4 a^2+9 b^2+4 c^2+6 a b-6 b c+4 c a\right)$
$=8 a^3-27 b^3-8 c^3-36 a b c$

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 Identities→Algebraic Identities — all question types→Maths STD 9 question papers→Gujarat Board STD 9 question papers→Gujarat Board question paper generator→

Similar questions

If $x = 2a + 1$ and $y = a -1$ is a solution of the equation $2x - 3y + 5 = 0$, find the value of a.

Plot the following points and check whether they are collinear or not:
$(1, 1), (2, -3), (-1, -2)$

Find the length of $13.2\ kg$ of copper wire of diameter 4mm, when $1$ cubic centimetre of copper weighs $8.4g.$

Express the following decimals in the form $\frac{\text{p}}{\text{q}},$ where $p, q$ are integers and $\text{q}\neq0.$ $0.\overline{53}$

The monthly profits (in ₹) of $100$ shops are distributed as follows:

Profits per shop:	$0-50$	$50-100$	$100-150$	$150-200$	$200-250$	$250-300$
No. of shops:	$12$	$18$	$27$	$20$	$17$	$6$

Draw a histogram for the data and show the frequency polygon for it.

A metal cube of edge $12\ cm$ is melted and formed into three smaller cubes. If the edges of the two smaller cubes are $6\ cm$ and $8\ cm$, find the edge of the third smaller cube.

Factorise: $(a-3 b)^3+(3 b-c)^3+(c-a)^3$

Factorize: $x^3 + x - 3x^2 - 3$

Simplify the following products: $(\text{x}^2 +\text{x}- 2)(\text{x}^2-\text{x} + 2)$

It being given that $\sqrt{3}=1.732,\sqrt{5}=2.236,\sqrt{6}=2.449$ and $\sqrt{10}=3.162,$ find to three places of decimal, the value of the following: $\frac{6}{\sqrt{5}+\sqrt{3}}$