Question

गुणनखंड कीजिए : (i) $a^4- b^4$ (ii) $p^4- 81$ (iii) $x^4- (y + z)^4$ (iv) $x^4- (x - z)^4$ (v) $a^4- 2a^2b^2+ b^4$

Answer 1

Answer Explanation:

(i) a⁴ − b⁴  

= (a²)² − (b²)²

= (a² − b²) (a² + b²)

[(a² − b²) = (a − b) (a + b)]

= (a − b) (a + b) (a² + b²)

 

(ii) p⁴ − 81

= (p²)² -  (9)²

= (p² − 9) (p² + 9)

[(a² − b²) = (a − b) (a + b)]

= [(p)² − (3)²] (p² + 9)

= (p − 3) (p + 3) (p² + 9)

 

(iii)x⁴ − (y + z)⁴  

= (x²)² − [(y +z)²]²

= [x² − (y + z)²] [x² + (y + z)²]

[(a² − b²) = (a − b) (a + b)]

= [x − (y + z)][ x + (y + z)] [x² + (y + z)²]

= (x − y − z) (x + y + z) [x² + (y + z)²]

 

(iv)x⁴ − (x − z)⁴  

= (x²)² − [(x − z)²]²

= [x² − (x − z)²] [x² + (x − z)²]

[(a² − b²) = (a − b) (a + b)]

= [x − (x − z)] [x + (x − z)] [x² + (x − z)²]

= z(2x − z) [x² + x² − 2xz + z²]

= z(2x − z) (2x² − 2xz + z²)

 

(v)a⁴ − 2a²b² + b⁴

= (a²)² − 2 (a²) (b²) + (b²)²

= (a²− b²)²

= [(a − b) (a + b)]²

[(a² − b²) = (a − b) (a + b)]

= (a − b)² (a + b)²

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

इस पाठ से संबंधित कुछ और प्रश्न :

गुणनखंड कीजिए :  

(i) $4p^2- 9q^2$ (ii) $63a^2- 112b^2$ (iii) $49x^2- 36$ (iv) $16x^5- 144x^3$ (v) $(l + m)^2 -(l - m)^2$ (vi) $9x^2 y^2- 16$ (vii) $(x^2- 2xy + y^2) - z^2$ (viii) $25a^2- 4b^2+ 28bc - 49c^2$

https://brainly.in/question/10768006

निम्नलिखित व्यंजकों के गुणनखंड कीजिए :  

(i) $ax^2+ bx$ (ii) $7p^2+ 21q^2$ (iii) $2x^3+ 2xy^2+ 2xz^2$ (iv) $am^2+ bm^2+ bn^2+ an^2$ (v) $(lm + l) + m + 1$ (vi) $y (y + z) + 9 (y + z)$ (vii) $5y^2-20y - 8z + 2yz$ (viii) $10ab + 4a + 5b + 2$ (ix) $6xy - 4y + 6 - 9x$

https://brainly.in/question/10967776

Answer 2

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

(i) a⁴ − b⁴

= (a²)² − (b²)²

= (a² − b²) (a² + b²)

[(a² − b²) = (a − b) (a + b)]

= (a − b) (a + b) (a² + b²)

(ii) p⁴ − 81

= (p²)² - (9)²

= (p² − 9) (p² + 9)

[(a² − b²) = (a − b) (a + b)]

= [(p)² − (3)²] (p² + 9)

= (p − 3) (p + 3) (p² + 9)

(iii) x⁴ − (y + z)⁴

= (x²)² − [(y +z)²]²

= [x² − (y + z)²] [x² + (y + z)²]

[(a² − b²) = (a − b) (a + b)]

= [x − (y + z)][ x + (y + z)] [x² + (y + z)²]

= (x − y − z) (x + y + z) [x² + (y + z)²]

(iv) x⁴ − (x − z)⁴

= (x²)² − [(x − z)²]²

= [x² − (x − z)²] [x² + (x − z)²]

[(a² − b²) = (a − b) (a + b)]

= [x − (x − z)] [x + (x − z)] [x² + (x − z)²]

= z(2x − z) [x² + x² − 2xz + z²]

= z(2x − z) (2x² − 2xz + z²)

(v) a⁴ − 2a²b² + b⁴

= (a²)² − 2 (a²) (b²) + (b²)²

= (a²− b²)²

= [(a − b) (a + b)]²

[(a² − b²) = (a − b) (a + b)]

= (a − b)² (a + b)²