Simplify : $4((\frac{6}{4})x^2 – 25 x + 12) – 6 (x^2 + 5x – 13). $

Let’s simplify step by step:

Given expression:
$4\left(\frac{6}{4}x^2 - 25x + 12\right) - 6(x^2 + 5x - 13)$

Step 1: Simplify inside brackets

$\frac{6}{4}x^2 = \frac{3}{2}x^2$

So expression becomes:
$4\left(\frac{3}{2}x^2 - 25x + 12\right) - 6(x^2 + 5x - 13)$

Step 2: Multiply terms

First bracket:
$4 \times \frac{3}{2}x^2 = 6x^2$
$4 \times (-25x) = -100x$
$4 \times 12 = 48$

So:
$6x^2 - 100x + 48$

Second bracket:
$-6(x^2 + 5x - 13) = -6x^2 - 30x + 78$

Step 3: Combine like terms

$(6x^2 - 100x + 48) + (-6x^2 - 30x + 78)$

• $6x^2 - 6x^2 = 0$
• $-100x - 30x = -130x$
• $48 + 78 = 126$

Final Answer:

-130x + 126