Use the identity x - a x - b - x 2- a - b x - ab to find the following products-a b c-4a b c-2A- a2 b2 c2-6 a b c-8B- a2 b2 c2-6 a b c-8C- a2 b2 c2-6 a-8D- a2 b2 c2-6 a-8

The correct option is B a^2b^2c^2 6abc + 8 ⇒ (abc 4)(abc 2) =(abc)^2 + ( 4 2)× abc +( 4) × ( 2) nbsp; [Using identity (x+a) (x+b) =x^2 + (a+b).x + ...

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Byju's Answer

Standard VIII

Mathematics

Expansion of (x+a)(x+b)

Use the ident...

Question

Use the identity $(x + a) (x + b) = x^{2} + (a + b) x + a b$ to find the following products:
$(a b c - 4) (a b c - 2)$

$a^{2} b^{2} c^{2} - 6 a b c - 8$

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$a^{2} b^{2} c^{2} - 6 a b c + 8$

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$a^{2} b^{2} c^{2} + 6 a + 8$

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$a^{2} b^{2} c^{2} - 6 a - 8$

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Solution

The correct option is B
$a^{2} b^{2} c^{2} - 6 a b c + 8$

$\Rightarrow (a b c - 4) (a b c - 2)$
$= (a b c)^{2} + (- 4 - 2) \times a b c + (- 4) \times (- 2)$ $[U s i n g i d e n t i t y (x + a) (x + b) = x^{2} + (a + b) . x + a b]$
$= a^{2} b^{2} c^{2} - 6 a b c + 8$

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Similar questions

Q. Use the identity

(x + a) (x + b) = x^{2} + (a + b) x + a b

to find the following products:
(xyz-4) (xyz-2)

Q. If

∣ ∣ ∣ ∣ \begin{matrix} a_{1} & b_{1} & c_{1} a_{2} & b_{2} & c_{2} a_{3} & b_{3} & c_{3} \end{matrix} ∣ ∣ ∣ ∣

= x

then

∣ ∣ ∣ ∣ \begin{matrix} a_{1} & b_{1} & c_{1} a_{2} & b_{2} & c_{2} a_{3} & b_{3} & c_{3} \end{matrix} ∣ ∣ ∣ ∣

∣ ∣ ∣ ∣ \begin{matrix} a_{1} & a_{2} & a_{3} b_{1} & b_{2} & b_{3} c_{1} & c_{2} & c_{3} \end{matrix} ∣ ∣ ∣ ∣

Q. Find the value of

\frac{a^{2} b^{2} c^{2}}{R^{2}}

in a right angled triangle.

Show that:

∣ ∣ ∣ ∣ \begin{matrix} a^{2} & b^{2} & c^{2} a & b & c 1 & 1 & 1 \end{matrix} ∣ ∣ ∣ ∣ = - (a - b) (b - c) (c - a)

Q. 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}

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Use the identity (x+a)(x+b)=x2+(a+b)x+ab to find the following products: (abc−4)(abc−2)

The correct option is B a2b2c2−6abc+8 ⇒(abc−4)(abc−2) =(abc)2+(−4−2)×abc+(−4)×(−2) [Using identity(x+a)(x+b)=x2+(a+b).x+ab] =a2b2c2−6abc+8

Use the identity $(x + a) (x + b) = x^{2} + (a + b) x + a b$ to find the following products:
$(a b c - 4) (a b c - 2)$

The correct option is B
$a^{2} b^{2} c^{2} - 6 a b c + 8$

$\Rightarrow (a b c - 4) (a b c - 2)$
$= (a b c)^{2} + (- 4 - 2) \times a b c + (- 4) \times (- 2)$ $[U s i n g i d e n t i t y (x + a) (x + b) = x^{2} + (a + b) . x + a b]$
$= a^{2} b^{2} c^{2} - 6 a b c + 8$