Question

व्यंजक के गुणनखंड कीजिए और निर्देशानुसार भाग दीजिए : (i) $(y^2 + 7y + 10) \div (y + 5)$ (ii) $(m^2- 14m - 32) \div (m + 2)$ (iii) $(5p^2- 25p + 20) \div (p - 1)$ (iv) $4yz(z^2+ 6z - 16) \div 2y(z + 8)$ (v) $5pq(p^2- q^2) \div 2p(p + q)$ (vi) $12xy(9x^2- 16y^2) \div 4xy(3x + 4y) (vii) 39y^3(50y^2- 98) \div 26y^2(5y + 7)$

Answer 1

Answer Explanation:

(i) (y² + 7y + 10) ÷ (y + 5)  

= (y² + 7y + 10)/(y + 5)

= [y² + (2 + 5)y + 10] / (y + 5)

= [y² + 2y + 5y + 10] / (y + 5)

= [y(y + 2) + 5(y + 2)]/(y + 5)

= [(y + 2)(y + 5)]/(y + 5)

= y + 2

 

(ii) (m² – 14m - 32) ÷ (m + 2)  

= (m² – 14m - 32) / (m + 2)

= [m² + (-16 + 2)m – 32)] /(m + 2)

= [m² – 16m + 2m – 32)] / (m + 2)  

= [m(m - 16) + 2(m – 16)] / (m + 2)

= [(m - 16)(m + 2)] / (m + 2)

= m + 2

 

(iii) (5p² – 25p + 20) ÷ (p - 1)  

= (5p² – 25p + 20)/(p - 1)

= 5(p² – 5p + 4) / (p - 1)

= 5[p² – (1 + 4)p + 4] / (p - 1)

= 5[p² – p - 4p + 4] / (p - 1)

= 5[p(p - 1) – 4(p - 1)] / (p - 1)

= 5[(p - 1)(p - 4)] /(p - 1)

= 5(p - 4)      

 

(iv) 4yz(z² + 6z - 16) ÷ 2y(z + 8)  

= [4yz(z² + 6z - 16)] / [2y(z + 8)]

= [4yz(z² + (8 - 2)z – 16)] / [2y(z + 8)]

= {4yz(z² + 8z - 2z – 16)} / {2y(z + 8)}

= [4yz{z(z + 8) – 2(z + 8)}] / [2y(z + 8)]

= [4yz(z + 8)(z - 2)] / [2y(z + 8)]

= 2z(z - 2)              

 

(v) 5pq(p² – q²) ÷ 2p(p + q)  

= [5pq(p² – q²)] / [2p(p + q)]

= [5pq(p – q)(p + q)] / [2p(p + q)]

= 5q(p – q)/2          

 

(vi) 12xy(9x² – 16y²) ÷ 4xy(3x + 4y)  

= 12xy{(3x)² – (4y)²} / {4xy(3x + 4y)}

12xy[(3x – 4y)(3x + 4y)] / [4xy(3x + 4y)]

=  3(3x – 4y)    

 

(vii) 39y³(50y² - 98) ÷ 26y²(5y + 7)  

= [39y³(50y² - 98)] / [26y²(5y + 7)]

= [39y³ 2(25y² - 49)] / [26y² (5y + 7)]

= [39y³ 2{(5y)² – 7²}] / [26y²(5y + 7)]

=[39y³ × 2{(5y - 7)(5y + 7)}] / [26y²(5y + 7)]

= [13 × 3y³ × 2{(5y - 7)(5y + 7)}] / [13 × 2y²(5y + 7)]

= 3y(5y - 7)

आशा है कि यह उत्तर आपकी अवश्य मदद करेगा।।।।  

इस पाठ से संबंधित कुछ और प्रश्न :

निम्नलिखित विभाजन कीजिए : (i) $(10x - 25) \div 5$ (ii) $(10x - 25) \div (2x - 5)$ (iii) $10y(6y + 21) \div 5(2y + 7)$ (iv) $9x^2y^2(3z - 24) \div 27xy(z - 8)$ (v) $96abc(3a - 12) (5b - 30) \div 144(a - 4) (b - 6)$

https://brainly.in/question/10768324

निर्देशानुसार भाग दीजिए : (i) $5(2x + 1) (3x + 5) \div (2x + 1)$ (ii) $26xy(x + 5) (y - 4) \div 13x(y - 4)$ (iii) $52pqr (p + q) (q + r) (r + p) \div 10^4pq(q + r) (r + p)$ (iv) $20(y + 4) (y^2+ 5y + 3) \div 5(y + 4)$ (v) $x(x + 1) (x + 2) (x + 3) \div x(x + 1)$

https://brainly.in/question/10768317

Answer 2

$\huge{\boxed{\red{\boxed{\mathfrak{\pink{Solution}}}}}}$

(i) (y² + 7y + 10) ÷ (y + 5)

= (y² + 7y + 10)/(y + 5)

= [y² + (2 + 5)y + 10] / (y + 5)

= [y² + 2y + 5y + 10] / (y + 5)

= [y(y + 2) + 5(y + 2)]/(y + 5)

= [(y + 2)(y + 5)]/(y + 5)

= y + 2

(ii) (m² – 14m - 32) ÷ (m + 2)

= (m² – 14m - 32) / (m + 2)

= [m² + (-16 + 2)m – 32)] /(m + 2)

= [m² – 16m + 2m – 32)] / (m + 2)

= [m(m - 16) + 2(m – 16)] / (m + 2)

= [(m - 16)(m + 2)] / (m + 2)

= m + 2

(iii) (5p² – 25p + 20) ÷ (p - 1)

= (5p² – 25p + 20)/(p - 1)

= 5(p² – 5p + 4) / (p - 1)

= 5[p² – (1 + 4)p + 4] / (p - 1)

= 5[p² – p - 4p + 4] / (p - 1)

= 5[p(p - 1) – 4(p - 1)] / (p - 1)

= 5[(p - 1)(p - 4)] /(p - 1)

= 5(p - 4)

(iv) 4yz(z² + 6z - 16) ÷ 2y(z + 8)

= [4yz(z² + 6z - 16)] / [2y(z + 8)]

= [4yz(z² + (8 - 2)z – 16)] / [2y(z + 8)]

= {4yz(z² + 8z - 2z – 16)} / {2y(z + 8)}

= [4yz{z(z + 8) – 2(z + 8)}] / [2y(z + 8)]

= [4yz(z + 8)(z - 2)] / [2y(z + 8)]

= 2z(z - 2)

(v) 5pq(p² – q²) ÷ 2p(p + q)

= [5pq(p² – q²)] / [2p(p + q)]

= [5pq(p – q)(p + q)] / [2p(p + q)]

= 5q(p – q)/2

(vi) 12xy(9x² – 16y²) ÷ 4xy(3x + 4y)

= 12xy{(3x)² – (4y)²} / {4xy(3x + 4y)}

12xy[(3x – 4y)(3x + 4y)] / [4xy(3x + 4y)]

= 3(3x – 4y)

(vii) 39y³(50y² - 98) ÷ 26y²(5y + 7)

= [39y³(50y² - 98)] / [26y²(5y + 7)]

= [39y³ 2(25y² - 49)] / [26y² (5y + 7)]

= [39y³ 2{(5y)² – 7²}] / [26y²(5y + 7)]

=[39y³ × 2{(5y - 7)(5y + 7)}] / [26y²(5y + 7)]

= [13 × 3y³ × 2{(5y - 7)(5y + 7)}] / [13 × 2y²(5y + 7)]

= 3y(5y - 7)