Question

सरल कीजिए : (i) $(x^2- 5) (x + 5) + 25$ (ii) $(a^2+ 5) (b^3+ 3) + 5$ (iii) $(t + s^2) (t^2- s)$ (iv) $(a + b) (c - d) + (a - b) (c + d) + 2 (ac + bd)$ (v) $(x + y)(2x + y) + (x + 2y)(x - y)$ (vi) $(x + y)(x^2- xy + y^2)$ (vii) $(1.5x - 4y)(1.5x + 4y + 3) - 4.5x + 12y$ (viii) $(a + b + c)(a + b - c)$

Answer 1

Answer with Step-by-step explanation:

i) दिया है : (x² - 5)(x + 5) + 25

= x²(x + 5) - 5(x + 5) + 25

= x³+ 5x² - 5x - 25 + 25

= x³ + 5x² - 5x

 

ii) (a² + 5)(b³ + 3) + 5

a²(b³ + 3) + 5(b³ + 3)

a²b³ + 3a² + 5b³ + 15 + 5

= a²b³ + 5b³ + 3a² + 20

 

iii) दिया है : (t + s²)(t² - s)

t(t² - s) + s²(t² - s)

t³- ts + s²t² - s³

 

iv) दिया है : (a + b)(c - d) + (a - b)(c + d) + 2(ac + bd)

a(c - d) + b(c - d) + a(c + d) - b(c + d) + 2(ac + bd)

(ac - ad + bc - bd) + (ac + ad - bc - bd) + (2ac + 2bd)

= ac - ad + bc - bd + ac + ad - bc - bd + 2ac + 2bd

= ac + ac + 2ac - ad + ad + bc - bc - bd - bd + 2bd

= 4ac

 

v) दिया है : (x + y) (2x + y) + (x + 2y) (x − y)

= x(2x + y)+y(2x + y) + x(x-y)+2y(x-y)

=2x² + xy + 2xy + y² + x² - xy + 2xy - 2y²

= 2x² + x² + xy - xy + 2xy + 2xy + y² - 2y²

= 3x² + 4xy - y²

 

vi) दिया है : (x + y) (x² − xy + y²)  

x(x² − xy + y²)  +y(x² -xy+y²)

= x³- x²y + xy² + x²y – xy² +y³

= x³ - x²y + x²y + xy² - xy² + y³

= x³ + y³

 

 vi) दिया है : (1.5x − 4y) (1.5x + 4y + 3) − 4.5x + 12y

= 1.5x(1.5x + 4y + 3) -4y(1.5x + 4y + 3) - 4.5x + 12y

= .25x² + 6xy + 4.5x - 6xy - 16y² - 12y - 4.5x + 12y

= 2.25x² + 6xy - 6xy + 4.5x - 4.5x - 12y + 12y - 16y²

= 2.25x² - 16y²

 

 

vii) दिया है : (a + b + c) (a + b − c)

= a(a + b − c)+b(a + b − c)+c(a + b − c)

= a² + ab - ac + ab + b² - bc + ac + bc - c²

= a² + ab + ab - ac + ac + b² - c² + bc - bc

= a² + 2ab + b² - c²

आशा है कि यह उत्तर आपकी मदद करेगा।।।।

इस पाठ से संबंधित कुछ और प्रश्न :

द्विपदों को गुणा कीजिए : (i) $(2x + 5)$ और $(4x - 3)$ (ii) $(y - 8)$ और $(3y - 4)$ (iii) $(2.5l - 0.5m)$ और $(2.5l + 0.5m)$ (iv) $(a + 3b)$ और $(x + 5)$ (v) $(2pq + 3q^2)$ और$(3pq - 2q^2)$ (vi) $(\frac{3}{4} a^2+3b^2)$ और $4(a^2-\frac{2}{3} b^2)$

https://brainly.in/question/11090082

गुणनफल ज्ञात कीजिए : (i) $(5 - 2x) (3 + x)$ (ii) $(x + 7y) (7x - y)$ (iii) $(a^2+ b) (a + b^2)$ (iv) $(p^2-q^2) (2p + q)$

https://brainly.in/question/11090119

Answer 2

Answer:

Step-by-step explanation:

(x² - 5)(x + 5) + 25

= x²(x + 5) - 5(x + 5) + 25

= x³+ 5x² - 5x - 25 + 25

= x³ + 5x² - 5x

ii) (a² + 5)(b³ + 3) + 5

a²(b³ + 3) + 5(b³ + 3)

a²b³ + 3a² + 5b³ + 15 + 5

= a²b³ + 5b³ + 3a² + 20

iii) : (t + s²)(t² - s)

t(t² - s) + s²(t² - s)

t³- ts + s²t² - s³

iv) : (a + b)(c - d) + (a - b)(c + d) + 2(ac + bd)

a(c - d) + b(c - d) + a(c + d) - b(c + d) + 2(ac + bd)

(ac - ad + bc - bd) + (ac + ad - bc - bd) + (2ac + 2bd)

= ac - ad + bc - bd + ac + ad - bc - bd + 2ac + 2bd

= ac + ac + 2ac - ad + ad + bc - bc - bd - bd + 2bd

= 4ac

v) : (x + y) (2x + y) + (x + 2y) (x − y)

= x(2x + y)+y(2x + y) + x(x-y)+2y(x-y)

=2x² + xy + 2xy + y² + x² - xy + 2xy - 2y²

= 2x² + x² + xy - xy + 2xy + 2xy + y² - 2y²

= 3x² + 4xy - y²

vi) : (x + y) (x² − xy + y²)

x(x² − xy + y²) +y(x² -xy+y²)

= x³- x²y + xy² + x²y – xy² +y³

= x³ - x²y + x²y + xy² - xy² + y³

= x³ + y³

vi) : (1.5x − 4y) (1.5x + 4y + 3) − 4.5x + 12y

= 1.5x(1.5x + 4y + 3) -4y(1.5x + 4y + 3) - 4.5x + 12y

= .25x² + 6xy + 4.5x - 6xy - 16y² - 12y - 4.5x + 12y

= 2.25x² + 6xy - 6xy + 4.5x - 4.5x - 12y + 12y - 16y²

= 2.25x² - 16y²

vii) : (a + b + c) (a + b − c)

= a(a + b − c)+b(a + b − c)+c(a + b − c)

= a² + ab - ac + ab + b² - bc + ac + bc - c²

= a² + ab + ab - ac + ac + b² - c² + bc - bc

= a² + 2ab + b² - c²