Question

simplify
(a) (x+y)(2x+y)+(x+2y)(x-y)
(b) (a+b+c) (a+b-c)
(c) (2y+5) (2y+5)
(d) (4n+5) (4n+1)
(e) (2n+5y) (2n+3y)

plz give the answer step by step.... plz fast​

Answer 1

Answer:

(a). (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

= (2+1)x² + (1+2−1+2)xy + (1−2)y²

= 3x² + 4xy – y²

(b). (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 – bc + bc – ac + ac + b²– c²

= a²+ 2ab + b² – c²+ 0 + 0

= a² + 2ab + b²– c²

(c). (2x+5)(2y+5)

= (2x × 2y +5 × 2y + 5 × 2x + 5 × 5)

= (4xy + 10x + 10y + 25)

(d). (4n+5) (4n+1)

= 4n (4n+1) + 5 (4n+1)

= 16 n² + 4n+ 5 (4n+1)

= 16 n² + 4n + 20n + 5

= 16n² + 24n + 5

(e). (2x+5y)(2x+3y).

We know, (x+a)(x+b)=x²+(a+b)x+ab

On comparing, we get,

x=2x,a=5y,b=3y.

Thus,

= (2x+5y) (2x+3y)

=(2x)² + (5y+3y) 2x + (5y) × (3y)

=4x² + (8y)2x + 15y²

=4x² + 16xy + 15y²