Question

Are the proof and the identity valid? if not, what is the invalid step in the proofStep 1: x (9x+3) +3(x+3)=9x²+6x+9Step 2: =(3x+3)²Step 3: =(3(x+1))²Step 4: =9(x+1)²A) the proof is validB) step 2 is not validC) step 1 is not validD) step 3 is not valid

Answer 1

Are the proof and the identity valid? if not, what is the invalid step in the proof

Step 1: x (9x+3) +3(x+3)=9x²+6x+9

Step 2: =(3x+3)²

Step 3: =(3(x+1))²

Step 4: =9(x+1)²



A) the proof is valid

B) step 2 is not valid

C) step 1 is not valid

D) step 3 is not valid​

Verify each step

step 1

x (9x+3) +3(x+3)

=9x^2+3x+3x+9

=9x^2+6x+9

step 1 is correct

step 2

Complete squares

9x^2+6x+9=0

Factor 9

9(x^2+6/9x)+9=0

9(x^2+2/3x)+9=0

9(x^2+2/3x+4/36-4/36)+9=0

9(x^2+2/3x+4/36)+9-1=0

9(x^2+2/3x+4/36)+8=0

9(x+2/6)^2=-8

therefore

step 2 is not valid