Class 7 Mathematics Exercise 4.1 Full Solution

(1) Solution:- (3abx 4³a)

= 12a⁴ b

(2) Solution:- (5xyx 6az)

= 30axyz.

(3) Solution:- (5ax ²X 3ax² y)

= 15a³ x⁷ y

(4) Solution:- 8a² b X (-2b²)

= -16a² b³

(5) Solution:- (-2abx²) x (10bx³ y z)

= -20ab⁴ x³ y z

(6) Solution:- (-3p² q³)x (-6p⁵ q⁴ )

= 18 p⁷q⁷

(7) Solution:- (-12m² a² x ²) x (-2ma² x²)

= 24 m³ a⁴ x⁵

(8) Solution:- (7a³ bx⁵ y²) x (-3x⁵ y⁵ a² b² )

= – 21a⁵ b³ x¹⁰y⁵

(9) Solution:- (2x+3y) (5xy)

= (10x² y +15xy²)

(10) Solution:- (5x- 4xy) (9x y)

= 45x y – 36 x y

(11) Solution:- (2a² – 3b²+c²) (a³ b²)

= 2a⁵ b² – 3a³ b⁴+ a³ b² c²

(12) Solution:- (x³ – y² + 3xyz) (x⁴ y)

= x⁷ y- x⁴ y³ + 3x⁵ y z

(13) Solution:- (2a-3b) (3a+2b)

= 6a² + 4ab- 9ab- 6b²

= 6a² – 5ab- 6b²

(14) Solution:- (a+ b) (a-b)

= a² –b²

(15) solution:- (x²+1) (x²-1)

= (x²)² – (11)²

= (x⁴-1)

(16) Solution:- (a+ b) (a+ b)

= a³+ a² b+ ab² +b³

(17) Solution:- (a² –a b +b²) (a +b)

= a³+ a² b – a² b – a b²+ a b²+ b³

= a³+b³

(18) Solution:- (x+2xy+y) 9x+y)

= x³+yx²+2x² y+2x² y+ xy² +y³

= x³+ 3x² y+ 3xy²+ y³

(19) Solution:- (x²-2xy+y²) (x-y)

= x²-x² y – 2x² y+2x y²+xy²-y³

= x³– 3xy²+ 3xy²– y³

(20) Solution:- (x+2x-3) (x+3)

= x³ + 3x² + 2x² +6x- 3x-9

= x³ + 5x²+ 3x-9

(21) Solution:- (a²+ab+ b²) (b²– ab+ a²)

= a² b² –a³b+a⁴ +ab³– a² b² +a³b+ b⁴-ab³+a² b²

= a⁴+b⁴+a² b²

(22) Solution:- (a+ b +c) (a+ b +c)

= (a + b + c)²

= a²+b²+c²+2ab+2bc+2ca

(23) Solution:- (x²-x³y +x² y²+ x³y- x² y² + xy³+ x² y² – xy³+y⁴)

= x⁴+ x² y² +y⁴

(24) Solution:- (y²-y+1) (1+y+y²)

= (y²+ y³+ y⁴-y- y^2- y³+1+y+ y²)

= y⁴+ y²+1

(25) Solution:-

A= x²+xy+y²

B= x-y

Therefore, L.H.S, AB

= (x²+xy+y²) (x-y)

= x³ – y3

= R.H.S

L.H.S=R.H.SS (proved).

(26) Solution:- AB.

= (a²-ab+b²) (a+ b)

= a³+b³

(27) Solution:- L.H.S,

(a²+1) (a – 1) (a²+1)

= (a²-1) (a²+1)

= (a²)² – (1)²

= a⁴ – 1

= R.H.S

(28) Solution:- L.H.S,

(x +y) (x-y) (x +y)

= (x²-y²) (x²+y²)

= (x²)² – (y²)²

= x⁴-y⁴

= R.H.S