so 2 consecutive numbers are number that come right after each other so the numbers could be represented as x and x+1 where x represents an unknown umber
squares are the number times itself so
x time x and (x+1) times (x+1)
so therefor the difference is 31
obviously (x+1) times (x+1) is bigger than x times x so
x times x=(x+1) times (x+1)-31
so you multiply to findn the answer
x times x=x^2
pemdas so multiply
(x+1)(x+1)
use distributive property which si a(b+c)=ab+ac so
(x+1)(x+1)=(x+1)(x)+(x+1)(1)
distribute again
(x+1)(x)=x^2+1x
(x+1)(1)=1x+1
(x+1)(x+1)=x^2+1x+1x+1=x^2+2x+1
so we have
x^2=x^2+2x+1-31
add like terms
x^2=x^2+2x-30
subtract x^2 from both sides
x^2-x^2=x^2-x^2+2x-30
0=0+2x-30
0=2x-30
add 30 to both sides
30=2x
divide both sides by 2
15=x
subsitute
x+1 is second number
15+1=16
the numbers are 15 and 16
their squares are 225 and 256
the numbers are 15 and 16