If $(x +1)^2 + (x + 2)^2 = 16,$ then what is the value of $4x^2 + 12 x + 40 $ ?

62

(x+1)²+(x+2)² 

x²+2x+1+x²+4x+4=16

Combining like terms gives:

2x²+6x+5=16

Subtracting 5 from both sides =

2x² + 6x = 11

Now adding 20 on both sides =

2x² + 6x + 20 = 11 + 20

2x² + 6x + 20 = 31

Multiply both sides by 2 to get the desired equation,

 4x² + 12x + 40 = 2 × 31

 4x² + 12x + 40 = 62