Question

Which of these statements is a valid perfect square trinomial?

Statement 1: x2 + 10x + 100 = (x − 10)2
Statement 2: a2 + 2ab + b2 = (a + b)2

Group of answer choices

Statement 1 and statement 2 are valid.

Statement 1 and statement 2 are invalid.

Only statement 1 is valid.

Only statement 2 is valid.

Answer 1

Statement 2 only

Explanation:

2nd one is the identity so no need to verify its true

1st one

• (x-10)²
• x²-20x+100

Hence wrong

Answer 2

• D. Only statement 2 is valid

Explanation:

Verify if the statements are correct

Statement 1:

• x² + 10x + 100 = (x − 10)²
• x² + 10x + 100 = x² + 2(x)(-10) + (-10)²
• x² + 10x + 100 = x² - 20x + 100
• LHS ≠ RHS

Statement 2:

• a² + 2ab + b² = (a + b)²
• a² + 2ab + b² = a² + 2ab + b²
• LHS = RSH

As we see the second statement is valid but not the first one.

Correct choice is D