Video Transcript
If 𝑢 is equal to 𝑥 plus four and 𝑢 is greater than or equal to zero. Which of the following is equivalent to 𝑥 minus three squared multiplied by the square root of 𝑥 plus four. Is it A) 𝑢 minus seven squared multiplied by the square root of 𝑢. B) 𝑢 minus four squared multiplied by the square root of 𝑢. C) 𝑢 minus three squared multiplied by the square root of 𝑢. Or D) 𝑢 plus one squared multiplied by the square root of 𝑢.
Our aim in this question is to find an expression that is equivalent to 𝑥 minus three squared multiplied by the square root of 𝑥 plus four in terms of 𝑢. We’re told that 𝑢 is equal to 𝑥 plus four. This means that we can replace the 𝑥 plus four in the second part of our expression with 𝑢. This gives us the square root of 𝑢. If 𝑢 is equal to 𝑥 plus four, then 𝑢 minus four is equal to 𝑥 as we can subtract four from both sides of the equation. This means that we can replace the 𝑥 in the first part of our expression with 𝑢 minus four. This means that the expression inside the bracket is 𝑢 minus four minus three. Negative four minus three is equal to negative seven. This means that we can simplify the bracket to 𝑢 minus seven.
The expression has now become 𝑢 minus seven squared multiplied by the square root of 𝑢. When 𝑢 is equal to 𝑥 plus four, then the expression 𝑥 minus three squared multiplied by the square root of 𝑥 plus four is equivalent to 𝑢 minus seven squared multiplied by the square root of 𝑢. The correct answer was option A.
