Question

Expand the following using the identies
(2m^+6n^)2​

Answer 1

Answer:

Here is your answer dear

Step-by-step explanation:

(i) (5x + 2y + 7) (5x + 2y + 3)

= {(5x + 2y) + 7} {(5x + 2y) + 3}

= (5x + 2y)2+ (7 + 3) (5x + 2y) + 7 x 3

{since (x + a) (x + b) = x2+ (a + b) x + a b }

= 25x2+ 4y2+2 × 5x × 2y + 10 (5x + 2y) + 21

= 25x2+ 4y2 + 20xy + 50x + 20y + 21

(ii) (3x - 7y + 3) (3x - 7y - 5)

= {(3x-7y)+3} {3x-7y)-5}

= (3x - 7y)2+ (3 - 5) (3x - 7y) + 3 × (-5)

={ (x + a) (x + b) = x2+ (a + b) x + a b }

= 9x2+ 49y2- 2 × 3x × 7y + (-2) (3x -7y) - 15

= 9x2+ 49y2 -42xy - 6x + 14y - 15

(iii) (4a - 5b - 8) (4a - 5b + 5)

= {(4a - 5b) - 8} {(4a - 5b) + 5}

= (4a - 5b)2+ (-8 + 5) (4a - 5b) + (-8) (5)

{since (x + a) (x + b) = x2+ (a +b) x + ab}

= 16a2+ 25b2- 2 × 4a × 5b + (-3)(4a - 5b) - 40

=16a2+ 25b2- 40ab - 12a + 15b - 40

(iv) (2m + 6n - 7) (2m + 6n - 6)

= {(2m + 6n) - 7} {(2m + 6n)- 6}

= (2m + 6n)2+ (-7 - 6) (2m + 6n) + (- 7) (-6)

{since (x + a) (x + b) = x2+ (a + b) x + ab}

= 4m2+ 36n2+ 2 × 2m × 6n + (-13) (2m + 6n) + 42

= 4m2+ 36n2+ 24mn - 26m - 78n + 42