\(\frac{2}{3}-\frac{5}{4}=\frac{8-15}{12}=\frac{-7}{12}\)
\(\frac{5}{4}-\frac{2}{3}=\frac{15-8}{12}=\frac{7}{12}\)
\(\therefore \frac{-7}{12} \ne \frac{7}{12}\)
\(\therefore \frac{2}{3}-\frac{5}{4} \ne \frac{5}{4}-\frac{2}{3}\)

700

(a² + 2b²) x (5a – 3b) = a² (5a – 3b) + 2b2 x (5a – 3b)
= 5a³ – 3a²b + 10ab² – 6b³

we have  81a⁴ - 16b⁴=(9a²)² - (4b²)²
= (9a² + 4b²)(9a² - 4b²) 
[Using A² - B² = (A + B)(A - B)]
= (9a² + 4b²)[(3a)² - (2b)²]
= (9a² + 4b²)[(3a + 2b)(3a - 2b)]
= (9a² + 4b²)(3a + 2b)(3a - 2b)

83^o each

70^o

80^o, 100^o, 80^o, 100^o

we have a⁴ + 2a²b² + b⁴
= (a²)² + 2(a²)(b²) + b²)²
= (a²+b²)² = (a²+b²)(a² + b²)
∴ a⁴ + 2a²b²+b²
=(a² + b²)² = (a² + b²)(a² + b²)

243 = 3 x 3 x 3 x 3 x 3
In the above factorisation 3 x 3 remains after grouping the 3’s in triplets. Therefore, 243 is not a perfect cube.

\(\left(\frac{2}{3}\right)^{-2}=\frac{2^{-2}}{3^{-2}}=\frac{3^{2}}{2^{2}}=\frac{9}{4}\)

Cuboid;
(i) 6
(ii) 6
(iii) 12

∵ The ends (bases) of the given solid are congruent rectilinear figure each of six sides.
∴ It is a hexagonal prism.
In a hexagonal prism, we have:
The number of faces = 8
The number of edges = 18
The number of vertices = 12

We have to factorise both terms
x²y = x \(\times \) x \(\times \) y
and - xy² = -x \(\times \) y \(\times \) y
= -1 \(\times \) x \(\times \) y \(\times \) y
Common factor in both terms is x \(\times \) y.

(l +7)(l + m)

We have, 4.5 x 10⁴ = 4.5 x 10000 = 45000

300

The negative (or additive inverse) of \({-6\over-7}(={6\over7})={-6\over7}\)

we have,\(-1\times {-2\over5}={(-1)\times(-2)\over5}={2\over5}\)
\(\therefore\)The multiplicative inverse of \(-1\times {-2\over5}\)is \(5\over2\)

= \(\frac { 2 }{ 5 } \times \left( \frac { -3 }{ 7 } \right) -\frac { 1 }{ 4 } +\frac { 1 }{ 14 } \times \frac { 2 }{ 5 } \)
= \(\frac { 2 }{ 5 } \times \left( \frac { -3 }{ 7 } \right) +\frac { 1 }{ 14 } \times \frac { 2 }{ 5 } -\frac { 1 }{ 4 } \) (Using commutativity)
= \(\frac { 2 }{ 5 } \left[ \frac { -3 }{ 7 } +\frac { 1 }{ 14 } \right] -\frac { 1 }{ 4 } \) (using distributivity)
= \(\frac { 2 }{ 5 } \left[ \frac { -6+1 }{ 14 } \right] -\frac { 1 }{ 4 } =\frac { 2 }{ 5 } \times \frac { -5 }{ 14 } -\frac { 1 }{ 4 } \)
= \(\frac { -1 }{ 7 } -\frac { 1 }{ 4 } =\frac { -4-7 }{ 28 } =\frac { -11 }{ 28 } \)