### 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’. Weβre 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.