Question

Expand ( 2x + 1)^3 , (5x + 7 + 2 )^2

Answer 1

(2x+1)³

=(2x) ³+1+3(2x)²(1)+3(2x)(1)²

=27x³+1+12x²+6x

=27x³+12x²+6x+1


(5x+7+2)²

=(5x+9)²

=(5x) ²+9²+2(5x)(9)

=25x²+81+90x

=25x²+90x+81

Answer 2

(a + b)^3 = a^3 + b^3 +3ab(a + b)
( 2x + 1)^3 = (2x)^3 + 1^3 + 3 x 2x x 1 (2x + 1)
                   = 8x^3 + 1 + 6x(2x +1)
                   = 8x^3 + 1 + 12x^2 + 6x

(a + b + c)^2 = a^2 + b^2 + c^2 +2ab + 2bc +2ca)
(5x + 7 + 2)^2 = (5x)^2 + (7)^2 + (2)^2 +( 2 x 5x x 7 ) + (2 x 7 x 2 )+ (2 x 2 x 5x) 
                       = 25x^2 + 49 + 4 + 70x + 28 + 20x
                       = 25x^2 + 20x + 70x + 49 + 4 + 28
                       = 25^3 + 90x + 81

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