MCQ
The product $(a+b)(a-b)\left(a^2-a b+b^2\right)\left(a^2+a b+b^2\right)$ is equal to:
- A$a^6+b^6$
- ✓$a^6-b^6$
- C$a^3-b^3$
- D$a^3+b^3$
✓
Answer
Correct option: B.
$a^6-b^6$
$(a+b)(a-b)\left(a^2-a b+b^2\right)\left(a^2+a b+b^2\right)$
$\left(a^2-b^2\right)\left(a^2+b^2-a b\right)\left(a^2+b^2-a b\right)$
$=\left(a^2-b^2\right)$ $\Big\{$$\left(a^2+b^2\right)^2-(a b)^2$$\Big\}$
$=\left(a^2-b^2\right)\left\{a^4+b^4+2 a^2 b^2-a^2 b^2\right\}$
$=\left(a^2-b^2\right)\left\{a^4+b^4+a^2 b^2\right\}$
$=\left\{a^6+a^2 b^4+a^4 b^2-b^2 a^4-b^6-b^4 a^2\right\}$
$=a^6-b^6$
Hence, correct option is$ (b).$
$\left(a^2-b^2\right)\left(a^2+b^2-a b\right)\left(a^2+b^2-a b\right)$
$=\left(a^2-b^2\right)$ $\Big\{$$\left(a^2+b^2\right)^2-(a b)^2$$\Big\}$
$=\left(a^2-b^2\right)\left\{a^4+b^4+2 a^2 b^2-a^2 b^2\right\}$
$=\left(a^2-b^2\right)\left\{a^4+b^4+a^2 b^2\right\}$
$=\left\{a^6+a^2 b^4+a^4 b^2-b^2 a^4-b^6-b^4 a^2\right\}$
$=a^6-b^6$
Hence, correct option is$ (b).$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
How many linear equation in x and $y$ can be satisfied by $x = 1$ and $y = 2?$
→What fraction of the whole circle is minor arc $RP$ in the given figure$?$
→If $x+a$ is a factor of $x^4-a^2 x^2+3 x-6 a$, then $a$ is:
→Line segments AB and CD intersect at O such that AC|| DB . If $\angle C A B=45^{\circ}$ and $\angle C D B=55^{\circ}$, then $\angle B O D=$
→If the base radius and the height of a right circular cone are increased by $20 \%$, then the percentage increase in volume is approximately:
→The diameters of two cones are equal. If their slant heights are in the ratio $5 : 4$, the ratio of their curved surface areas, is:
→An exterior angle of a triangle is $80^\circ $ and two interior opposite angles are equal. Measure of each of these angles is:
→Write the correct answer in the following:
The edges of a triangular board are $6 \mathrm{~cm}, 8 \mathrm{~cm}$ and $10\ cm$. The cost of painting it at the rate of $9$ paise per $\mathrm{cm}^2$ is:
→The edges of a triangular board are $6 \mathrm{~cm}, 8 \mathrm{~cm}$ and $10\ cm$. The cost of painting it at the rate of $9$ paise per $\mathrm{cm}^2$ is:
When $p(x) = x^3+a x^2+2 x+a$ is divided by $x + a,$ the remainder is:
→Write the correct answer in the following: Thales belongs to the country: