Question

निम्नलिखित व्यंजकों के गुणनखंड कीजिए : (तीनों पदों को मिलाने पर)। (i) $7x - 42$ (ii) $6p - 12q$ (iii) $7a^2 + 14a$ (iv) $- 16 z + 20 z^3$ (v) $20 l^2 m + 30 a l m$ (vi) $5 x^2y - 15 xy^2$ (vii) $10 a^2- 15 b^2+ 20 c^2$ (viii) $-4 a^2+ 4 ab - 4 ca$ (ix) $x^2y z + x y^2z + x y z^2$

Answer 1

Answer Explanation:

1) 7x -  42

=  (7× x) – (7×6)

= 7(x - 6)

 

2) 6p -12q

=  (6×p) – (6×2q)

= 6(p - 2q)

 

3) 7a²+14a

=(7×a×a) +  (2×7×a)

= 7a(a + 2)

 

4) -16z+ 20z³

= -(2 x 2 x 2 x 2 x z) + (2 x 2 x 5 x z x z x z)

= (2 x 2x z)  [ - (2 x 2) +( 5 x z x z)]

= 4z(- 4 + 5z²)

 

5) 20 l² m + 30 a l m

= (2×2×5×l×m×l) + (2×3×5×a×l×m)

= 2 x 5lm (2l + 3a)

= 2 x 5lm (2l + 3a)

= 10lm(2l + 3a)

 

6) 5 x²y -15 xy²

=(5×x×x×y)  + (5×3×x×y×y)

= 5xy(x - 3y)

 

7) 10a² -15 b²+20c²

= (2×5×a×a)  - (5×3×b×b) + (5×2×2×c×c)

= 5(2a² - 3b² + 4c²)

 

8) - 4a² + 4ab - 4ca

=(-4×a×a)  +(4×b×a) - (4×c×a)

= -4a(a - b + c)

 

9)  x²yz + xy²z  +xyz²

=(x×x×y×z)  +(x×y×y×z) +(x×y×z×z)

=xyz(x + y + z)

 

10) ax²y + bxy²  +cxyz

=(x×x×y×a)  +(x×y×y×b) +(x×y×z×c)

=xy(ax + by + cz)

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

इस पाठ से संबंधित कुछ और प्रश्न :

दिए हुए पदों में सार्व गुणनखंड ज्ञात कीजिए : (i) $12x,\ 36$ (ii) $2y,\ 22xy$ (iii) $14 pq, 28p^2q^2$ (iv) $2x, 3x^2, 4$ (v) $6 abc, 24ab^2, 12 a^2b$ (vi) $16 x^3, - 4x^2, 32x$ (vii) $10 pq, 20qr, 30rp$ (viii) $3x^2y^3, 10x^3y^2,6 x^2y^2z$

https://brainly.in/question/10767713

गुणनखंड कीजिए : (i) $x^2+ x y + 8x + 8y$ (ii) $15 xy - 6x + 5y - 2$ (iii) $ax + bx - ay - by$ (iv) $15 pq + 15 + 9q + 25p$ (v) $z - 7 + 7 x y - x y z$

https://brainly.in/question/10768017

Answer 2

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

1) 7x - 42

= (7× x) – (7×6)

= 7(x - 6)

2) 6p -12q

= (6×p) – (6×2q)

= 6(p - 2q)

3) 7a²+14a

=(7×a×a) + (2×7×a)

= 7a(a + 2)

4) -16z+ 20z³

= -(2 x 2 x 2 x 2 x z) + (2 x 2 x 5 x z x z x z)

= (2 x 2x z) [ - (2 x 2) +( 5 x z x z)]

= 4z(- 4 + 5z²)

5) 20 l² m + 30 a l m

= (2×2×5×l×m×l) + (2×3×5×a×l×m)

= 2 x 5lm (2l + 3a)

= 2 x 5lm (2l + 3a)

= 10lm(2l + 3a)

6) 5 x²y -15 xy²

=(5×x×x×y) + (5×3×x×y×y)

= 5xy(x - 3y)

7) 10a² -15 b²+20c²

= (2×5×a×a) - (5×3×b×b) + (5×2×2×c×c)

= 5(2a² - 3b² + 4c²)

9) x²yz + xy²z +xyz²

=(x×x×y×z) +(x×y×y×z) +(x×y×z×z)

=xyz(x + y + z)

10) ax²y + bxy² +cxyz

=(x×x×y×a) +(x×y×y×b) +(x×y×z×c)

=xy(ax + by + cz)