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

62 74 56 52

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