Work out the value of 3p − 4t², when p = 6 and t = 5 - Junior Cycle Mathematics - Question 5 - 2023

To multiply out and simplify the expression, use the distributive property:

1. Start with the given expression:

   $(2x - 3)(4 - 5x + x^2)$

2. Distribute (2x) to each term in the second parentheses:

   $2x(4) - 2x(5x) + 2x(x^2) = 8x - 10x^2 + 2x^3$

3. Now distribute (-3) to each term:

   $-3(4) + 3(5x) - 3(x^2) = -12 + 15x - 3x^2$

4. Combine all terms:

   $2x^3 - 10x^2 + 15x - 12$

The simplified expression is:

$2x^3 - 10x^2 + 15x - 12$

To factorise the expression, identify and factor out the common factors:

1. Start with the expression:

   $10de - df - 5ef + 2d^2$

2. Group terms to find common factors:

   $(10de + 2d^2) + (-df - 5ef)$

3. Factor each group:

   $2d(5e + d) - f(d + 5e)$

4. Notice the common factor $(d + 5e)$:

   $\Rightarrow (d + 5e)(2d - f)$

Thus, the fully factorised form is:

$(d + 5e)(2d - f)$