Class 7 Mathematics Exercise 5.2 Full Solution

(1) Solution:- (4x+3) (4x-3)

= (4x)² – (3)²

= 16x² -9

(2) Solution:- (13-12p) (13+12p)

= (13)² – (12p)²

= 169 – 144p²

(3) Solution:- (ab+3) (ab-3)

= (a b)² – (3)²

= a² b² – 9

(4) Solution:- (10-xy) (10+xy)

= (10)² – (x y)²

= 100 – x²y²

(5) Solution:- (4x²+3y²) (4x²-3y²)

= (4x²)² – (3y²)²

= 16x⁴– 9y⁴

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

= a- (b +c)}{a+ (b +c)}

= {a +(b +c)} {a- (b +c)}

= a2- (b +c)²

= a²– (b²+2bc+c²)

= a²-b² -2bc-c²

(8) Solution:- (x-1/2a) (x-5/2a)

= x2+ (-1/2a – 5/2a) x + (-1/2 a) (-5/2a)

= x2+ (-a-5a/2)x + 5a2/4

= x2+ (-6a/2)x + 4a2+4

= x2- 3ax + 5/4a2

(9) Solution:- (1/4x – 1/3y) (1/4x + 1/3y)

= (1/4x)2 – (1/3y)2

= x2/16 – y2/9

(10) Solution:- (a⁴+3a² x²+ 9x⁴) (9x⁴– 3a² x² + a⁴)

= {(a⁴+9x⁴) + 3a² x²} {a⁴+ 9x⁴) – 3a² x²}

= (a⁴+9x⁴)² – (3a²n²)²

= (a⁴)²+ 2x2a⁴x9x⁴+ (9x⁴)² – 9a⁴x⁴

= a⁸+ 18a⁴ x⁴ + 81x⁸– 9 a⁴ x 4⁴

(11) Solution:- (x+1) (x-1) (x²+1)

= (x²-1) (x²+1)

= (x2)² – (1)²

= x⁴-1

(12) Solution:- (9a²+b²) (3a+b) (3a-b)

= (9a²+b²) (9a² – b²)

= (9a²)² – (b²) ²

= 81a⁴ – b⁴