# Video: US-SAT04S4-Q25-590132562152

If π’ = π₯ + 4 and π’ β₯ 0. Which of the following is equivalent to (π₯ β 3)Β² βπ₯ + 4. [A] (π’ β 7)Β² βπ’ [B] (π’ β 4)Β² βπ’ [C] (π’ β 3)Β² βπ’ [D] (π’ + 1)Β² βπ’.

02:16

### Video Transcript

If π’ is equal to π₯ plus four and π’ is greater than or equal to zero. Which of the following is equivalent to π₯ minus three squared multiplied by the square root of π₯ plus four. Is it A) π’ minus seven squared multiplied by the square root of π’. B) π’ minus four squared multiplied by the square root of π’. C) π’ minus three squared multiplied by the square root of π’. Or D) π’ plus one squared multiplied by the square root of π’.

Our aim in this question is to find an expression that is equivalent to π₯ minus three squared multiplied by the square root of π₯ plus four in terms of π’. Weβre told that π’ is equal to π₯ plus four. This means that we can replace the π₯ plus four in the second part of our expression with π’. This gives us the square root of π’. If π’ is equal to π₯ plus four, then π’ minus four is equal to π₯ as we can subtract four from both sides of the equation. This means that we can replace the π₯ in the first part of our expression with π’ minus four. This means that the expression inside the bracket is π’ minus four minus three. Negative four minus three is equal to negative seven. This means that we can simplify the bracket to π’ minus seven.

The expression has now become π’ minus seven squared multiplied by the square root of π’. When π’ is equal to π₯ plus four, then the expression π₯ minus three squared multiplied by the square root of π₯ plus four is equivalent to π’ minus seven squared multiplied by the square root of π’. The correct answer was option A.