If $(x +1)^2 + (x + 2)^2 = 16,$ then what is the value of $4x^2 + 12 x + 40 $ ?
Answer & explanation
Correct answer: option 1
(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