Using Suitable Identity, Evaluate (97)3 - Mathematics

Using suitable identity, evaluate (97)³

योग

(97)³= (100 - 3)³= (100)³ - (3)³ - 3 × 100 × 3(100 - 3)
= 1000000 - 27 - 900 × 97
= 1000000 - 27 - 87300
= 912673

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Special Product

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अध्याय 4: Expansions (Including Substitution) - Exercise 4 (E) [पृष्ठ ६६]

अध्याय 4 Expansions (Including Substitution)
Exercise 4 (E) | Q 3.2 | पृष्ठ ६६

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

Simplify using following identity : `( a +- b )(a^2 +- ab + b^2) = a^3 +- b^3`
( 2x + 3y )( 4x² + 6xy + 9y²)

Simplify using following identity : `( a +- b )(a^2 +- ab + b^2) = a^3 +- b^3`
`( 3x - 5/x )( 9x^2 + 15 + 25/x^2)`

Simplify using following identity : `( a +- b )(a^2 +- ab + b^2) = a^3 +- b^3`
`(a/3 - 3b)(a^2/9 + ab + 9b^2)`

Find : (a + b)(a + b)(a + b)

Find : (a - b)(a - b)(a - b)

If a + b = 11 and a² + b² = 65; find a³ + b³.

If x = 3 + 2√2, find :
(i) `1/x`

(ii) `x - 1/x`

(iii) `( x - 1/x )^3`

(iv) `x^3 - 1/x^3`

Simplify :
`[(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 :
`[1.2 xx 1.2 + 1.2 xx 0.3 + 0.3 xx 0.3 ]/[ 1.2 xx 1.2 xx 1.2 - 0.3 xx 0.3 xx 0.3]`