Using suitable identity, evaluate : (i) (104) 3 (ii) (97) 3

(i) Given, ⇒ (104) 3 ⇒ (100 + 4) 3 Using identity : (a + b) 3 = a 3 + b 3 + 3ab(a + b) ⇒ (100 + 4) 3 = (100) 3 + 4 3 + 3 × 100 × 4 × (100 + 4) ⇒ (100 + 4) 3 = 1000000 + 64 + 124800 ⇒ 1124864. Hence, (104) 3 = 1124864. (ii) Given, ⇒ (97) 3 ⇒ (100 - 3) 3 ⇒ (100) 3 - 3 3 - 3 × 100 × 3 × (100 - 3) ⇒ 1000000 - 27 - 900 × 97 ⇒ 1000000 - 27 - 87300 ⇒ 912673. Hence, (97) 3 = 912673.

Mathematics

Using suitable identity, evaluate :
(i) (104)³
(ii) (97)³

Expansions

7 Likes

Answer

(i) Given,

⇒ (104)³

⇒ (100 + 4)³

Using identity :

(a + b)³ = a³ + b³ + 3ab(a + b)

⇒ (100 + 4)³ = (100)³ + 4³ + 3 × 100 × 4 × (100 + 4)

⇒ (100 + 4)³ = 1000000 + 64 + 124800

⇒ 1124864.

Hence, (104)³ = 1124864.

(ii) Given,

⇒ (97)³

⇒ (100 - 3)³

⇒ (100)³ - 3³ - 3 × 100 × 3 × (100 - 3)

⇒ 1000000 - 27 - 900 × 97

⇒ 1000000 - 27 - 87300

⇒ 912673.

Hence, (97)³ = 912673.

Answered By

6 Likes

Mathematics

Using suitable identity, evaluate :
(i) (104)³
(ii) (97)³

Expansions

Answer

Related Questions

Simplify (x + 6)(x - 4)(x - 2)

Simplify using following identity;
(a $\pm$ b)(a² $\mp$ ab + b²) = a³ $\pm$ b³
(i) (2x + 3y)(4x² - 6xy + 9y²)
(ii) $\Big(\dfrac{a}{3} - 3b\Big)\Big(\dfrac{a^2}{9} + ab + 9b^2\Big)$

Simplify :
$\dfrac{(x^2 - y^2)^3 + (y^2 - z^2)^3 + (z^2 - x^2)^3}{(x - y)^3 + (y- z)^3 + (z - x)^3}$

Evaluate:
$\dfrac{0.8 \times 0.8 \times 0.8 + 0.5 \times 0.5 \times 0.5}{0.8 \times 0.8 - 0.8 \times 0.5 + 0.5 \times 0.5}$

Mathematics

Using suitable identity, evaluate :(i) (104)3(ii) (97)3

Expansions

Answer

Related Questions

Simplify (x + 6)(x - 4)(x - 2)

Simplify using following identity;(a ±\pm± b)(a2 ∓\mp∓ ab + b2) = a3 ±\pm± b3(i) (2x + 3y)(4x2 - 6xy + 9y2)(ii) (a3−3b)(a29+ab+9b2)\Big(\dfrac{a}{3} - 3b\Big)\Big(\dfrac{a^2}{9} + ab + 9b^2\Big)(3a​−3b)(9a2​+ab+9b2)

Simplify :(x2−y2)3+(y2−z2)3+(z2−x2)3(x−y)3+(y−z)3+(z−x)3\dfrac{(x^2 - y^2)^3 + (y^2 - z^2)^3 + (z^2 - x^2)^3}{(x - y)^3 + (y- z)^3 + (z - x)^3}(x−y)3+(y−z)3+(z−x)3(x2−y2)3+(y2−z2)3+(z2−x2)3​

Evaluate:0.8×0.8×0.8+0.5×0.5×0.50.8×0.8−0.8×0.5+0.5×0.5\dfrac{0.8 \times 0.8 \times 0.8 + 0.5 \times 0.5 \times 0.5}{0.8 \times 0.8 - 0.8 \times 0.5 + 0.5 \times 0.5}0.8×0.8−0.8×0.5+0.5×0.50.8×0.8×0.8+0.5×0.5×0.5​

Using suitable identity, evaluate :
(i) (104)³
(ii) (97)³

Simplify using following identity;
(a $\pm$ b)(a² $\mp$ ab + b²) = a³ $\pm$ b³
(i) (2x + 3y)(4x² - 6xy + 9y²)
(ii) $\Big(\dfrac{a}{3} - 3b\Big)\Big(\dfrac{a^2}{9} + ab + 9b^2\Big)$

Simplify :
$\dfrac{(x^2 - y^2)^3 + (y^2 - z^2)^3 + (z^2 - x^2)^3}{(x - y)^3 + (y- z)^3 + (z - x)^3}$

Evaluate:
$\dfrac{0.8 \times 0.8 \times 0.8 + 0.5 \times 0.5 \times 0.5}{0.8 \times 0.8 - 0.8 \times 0.5 + 0.5 \times 0.5}$