Question

(9x³-4x³+16y²-21x²y)÷(x-y)
Pls Solve It.​

Answer 1

HCF : Highest Common Factor of the given terms, in simple words those terms which are common factor of all the given terms.

So we will Factorise both terms.

Factorisation of First Term :

⇒ (4x³ + 3x²y - 9xy² + 2y³)

⇒ 4x³ + (7 - 4)x²y - (7 + 2)xy² + 2y³

⇒ 4x³ + 7x²y - 4x²y - 7xy² - 2xy² + 2y³

⇒ x²(4x + 7y) - xy(4x + 7y) - 2y²(x - y)

⇒ (x² - xy)(4x + 7y) - 2y²(x - y)

⇒ x(x - y)(4x + 7y) - 2y²(x - y)

⇒ (x - y)[x(4x + 7y) - 2y²]

⇒ (x - y)[4x² + 7xy - 2y²]

⇒ (x - y)[4x² + (8 - 1)xy - 2y²]

⇒ (x - y)[4x² + 8xy - xy - 2y²]

⇒ (x - y)[4x(x + 2y) - y(x + 2y)]

⇒ (x - y)(x + 2y)(4x - y)

Factorisation of Second Term :

⇒ (x² + xy - 2y²)

⇒ x² + (2 - 1)xy - 2y²

⇒ x² + 2xy - xy - 2y²

⇒ x(x + 2y) - y(x + 2y)

⇒ (x - y)(x + 2y)

⠀⠀⠀⠀⠀───────────────

• HCF of the given terms :

⇢ HCF = Common Factor

Common factor in both terms are (x - y) and (x + 2y)

⇢ HCF = (x + 2y)(x - y)

∴ Correct option is (1) (x + 2y)(x - y).

Answer 2

(9x³-4x³+16y³-21x²y)÷(x-y)

( 5x³+16y³-21x²y) ÷(x-y)

x-y ) 5x³-21x²y+16y³ ( 5x²-16xy-16y²

5x³- 5x²y

- +

-16x²y+16y³

-16x²y+16xy²

+ -

-16xy²+16y³

-16xy²+16y³

+ -

0

Answer : 5x²-16xy-16y²

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