10. Simplify fully - OCR - GCSE Maths - Question 10 - 2019 - Paper 2

To simplify the expression, we multiply the coefficients and add the exponents of 'a':

1. Multiply the coefficients:

   • $6 × 2 = 12$

2. Add the exponents of 'a':

   • The exponent for 'a' in 6a is 1, and in 2a² it is 2:
   • Thus, $a^{1 + 2} = a^{3}$

Therefore, the fully simplified expression is: $12a^{3}$

To make 'x' the subject of the formula, follow these steps:

1. Start with the equation: $y = x² - 1$

2. Add 1 to both sides: $y + 1 = x²$

3. Take the square root of both sides, remembering to consider both positive and negative roots: $x = ± ext{sqrt}(y + 1)$

Thus, 'x' can be expressed as: $x = ± ext{sqrt}(y + 1)$