Question

algebra (equate or simplify)
① $6x^{2}-3x=? 3x(2x-1)$ ② $6y + 8x=?$
$6x^{2}: 3x$
$6x^{2}-3x()$ $6x^{2}÷3x=2x$
$-3x÷3x=-1$ $3x(2x-1)$
③ $3a×4a=?$
④ $6x÷2x=?$

Explanation:

Step1: Factor out GCF of $6x^2-3x$

The greatest common factor of $6x^2$ and $3x$ is $3x$. Divide each term by $3x$:
$\frac{6x^2}{3x} = 2x$, $\frac{-3x}{3x} = -1$
So $6x^2 - 3x = 3x(2x - 1)$

Step2: Simplify $6y+8x$

Factor out the GCF of 6 and 8, which is 2:
$6y + 8x = 2(3y + 4x)$

Step3: Multiply $3a \times 4a$

Multiply coefficients and combine like variables:
$3 \times 4 = 12$, $a \times a = a^2$
So $3a \times 4a = 12a^2$

Step4: Divide $6x \div 2x$

Divide coefficients and cancel like variables ($x
eq 0$):
$\frac{6}{2} = 3$, $\frac{x}{x} = 1$
So $6x \div 2x = 3$

Answer:

1. $3x(2x - 1)$
2. $2(3y + 4x)$
3. $12a^2$
4. $3$