Question

solve (D² + 2D +1)y=0​

Answer 1

Answer:

1.1 Factoring d2-2d+1

The first term is, d2 its coefficient is 1 .

The middle term is, -2d its coefficient is -2 .

The last term, "the constant", is +1

Step-1 : Multiply the coefficient of the first term by the constant 1 • 1 = 1

Step-2 : Find two factors of 1 whose sum equals the coefficient of the middle term, which is -2 .

-1 + -1 = -2 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -1 and -1

d2 - 1d - 1d - 1

Step-4 : Add up the first 2 terms, pulling out like factors :

d • (d-1)

Add up the last 2 terms, pulling out common factors :

1 • (d-1)

Step-5 : Add up the four terms of step 4 :

(d-1) • (d-1)

Which is the desired factorization