Verify: (i) x³ + y³ + z³ – 3xyz = (x + y + z)(x² + y² + z² – xy – yz – zx)(ii) x³ – y³ = (x – y)(x² + xy + y²

(i) x 3 + y 3 = (x + y) (x 2 - xy + y 2 ) R.H.S = (x + y) (x 2 - xy + y 2 ) = (x)(x 2 - xy + y 2 ) + (y)(x 2 - xy + y 2 ) = x 3 - x 2 y + xy 2 + yx 2 - xy 2 + y 3 = x 3 + y 3 Hence, L.H.S = R.H.S (ii) x 3 - y 3 = (x - y) (x 2 + xy + y 2 ) R.H.S = (x - y) (x 2 + xy + y 2 ) = (x)(x 2 + xy + y 2 ) - (y)(x 2 + xy + y 2 ) = x 3 + x 2 y + xy 2 - yx 2 - xy 2 - y 3 = x 3 - y 3 Hence, L.H.S = R.H.S

Mathematics

Verify :
(i) x³ + y³ = (x + y) (x² - xy + y²)
(ii) x³ - y³ = (x - y) (x² + xy + y²)

Polynomials

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Answer

(i) x³ + y³ = (x + y) (x² - xy + y²)

R.H.S

= (x + y) (x² - xy + y²)

= (x)(x² - xy + y²) + (y)(x² - xy + y²)

= x³ - x²y + xy² + yx² - xy² + y³

= x³ + y³

Hence, L.H.S = R.H.S

(ii) x³ - y³ = (x - y) (x² + xy + y²)

R.H.S

= (x - y) (x² + xy + y²)

= (x)(x² + xy + y²) - (y)(x² + xy + y²)

= x³ + x²y + xy² - yx² - xy² - y³

= x³ - y³

Hence, L.H.S = R.H.S

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Mathematics

Verify :
(i) x³ + y³ = (x + y) (x² - xy + y²)
(ii) x³ - y³ = (x - y) (x² + xy + y²)

Polynomials

Answer

Related Questions

Evaluate the following using suitable identities:
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(ii) (102)³
(iii) (998)³

Factorise each of the following:
(i) 8a³ + b³ + 12a²b + 6ab²
(ii) 8a³ - b³ - 12a²b + 6ab²
(iii) 27 - 125a³ - 135a + 225a²
(iv) 64a³ - 27b³ - 144a²b + 108ab²
(v) 27p³ - $\dfrac{1}{216}$ - $\dfrac{9}{2}$ p² + $\dfrac{1}{4}$ p

Factorise each of the following:
(i) 27y³ + 125z³
(ii) 64m³ - 343n³

Factorise : 27x³ + y³ + z³ - 9xyz

Mathematics

Verify :(i) x3 + y3 = (x + y) (x2 - xy + y2)(ii) x3 - y3 = (x - y) (x2 + xy + y2)

Polynomials

Answer

Related Questions

Evaluate the following using suitable identities:(i) (99)3(ii) (102)3(iii) (998)3

Factorise each of the following:(i) 8a3 + b3 + 12a2b + 6ab2(ii) 8a3 - b3 - 12a2b + 6ab2(iii) 27 - 125a3 - 135a + 225a2(iv) 64a3 - 27b3 - 144a2b + 108ab2(v) 27p3 - 1216\dfrac{1}{216}2161​ - 92\dfrac{9}{2}29​p2 + 14\dfrac{1}{4}41​p

Factorise each of the following:(i) 27y3 + 125z3(ii) 64m3 - 343n3

Factorise : 27x3 + y3 + z3 - 9xyz

Verify :
(i) x³ + y³ = (x + y) (x² - xy + y²)
(ii) x³ - y³ = (x - y) (x² + xy + y²)

Evaluate the following using suitable identities:
(i) (99)³
(ii) (102)³
(iii) (998)³

Factorise each of the following:
(i) 8a³ + b³ + 12a²b + 6ab²
(ii) 8a³ - b³ - 12a²b + 6ab²
(iii) 27 - 125a³ - 135a + 225a²
(iv) 64a³ - 27b³ - 144a²b + 108ab²
(v) 27p³ - $\dfrac{1}{216}$ - $\dfrac{9}{2}$ p² + $\dfrac{1}{4}$ p

Factorise each of the following:
(i) 27y³ + 125z³
(ii) 64m³ - 343n³

Factorise : 27x³ + y³ + z³ - 9xyz