$$ \left. \begin{array} { l } { ( 5 a + 2 ) ( 3 a - 1 ) = } \ { ( x - 4 ) ( x - 2 ) = } \end{array} ight. $$

Question

$$ \left. \begin{array} { l } { ( 5 a + 2 ) ( 3 a - 1 ) = } \ { ( x - 4 ) ( x - 2 ) = } \end{array} ight. $$

UpStudy AI · Accepted Answer

Simplify the expression by following steps:
- step0: Multiply the terms:
  $$\left(5a+2\right)\left(3a-1\right)$$
- step1: Apply the distributive property:
  $$5a\times 3a-5a\times 1+2\times 3a-2\times 1$$
- step2: Multiply the terms:
  $$15a^{2}-5a+6a-2$$
- step3: Add the terms:
  $$15a^{2}+a-2$$
Expand the expression $$ (x - 4)(x - 2) $$
Simplify the expression by following steps:
- step0: Multiply the terms:
  $$\left(x-4\right)\left(x-2\right)$$
- step1: Apply the distributive property:
  $$x\times x-x\times 2-4x-\left(-4\times 2\right)$$
- step2: Multiply the terms:
  $$x^{2}-2x-4x-\left(-8\right)$$
- step3: Remove the parentheses:
  $$x^{2}-2x-4x+8$$
- step4: Subtract the terms:
  $$x^{2}-6x+8$$
Let's expand both expressions step by step.

1. **For the expression $$ (5a + 2)(3a - 1) $$**:
   - We apply the distributive property (also known as the FOIL method for binomials):
     $$
     (5a + 2)(3a - 1) = 5a \cdot 3a + 5a \cdot (-1) + 2 \cdot 3a + 2 \cdot (-1)
     $$
   - Calculating each term:
     - $$ 5a \cdot 3a = 15a^2 $$
     - $$ 5a \cdot (-1) = -5a $$
     - $$ 2 \cdot 3a = 6a $$
     - $$ 2 \cdot (-1) = -2 $$
   - Now, combine the like terms:
     $$
     15a^2 + (-5a + 6a) - 2 = 15a^2 + a - 2
     $$

So, the expanded form is:
   $$
   15a^2 + a - 2
   $$

2. **For the expression $$ (x - 4)(x - 2) $$**:
   - Again, we apply the distributive property:
     $$
     (x - 4)(x - 2) = x \cdot x + x \cdot (-2) + (-4) \cdot x + (-4) \cdot (-2)
     $$
   - Calculating each term:
     - $$ x \cdot x = x^2 $$
     - $$ x \cdot (-2) = -2x $$
     - $$ -4 \cdot x = -4x $$
     - $$ -4 \cdot (-2) = 8 $$
   - Now, combine the like terms:
     $$
     x^2 + (-2x - 4x) + 8 = x^2 - 6x + 8
     $$

So, the expanded form is:
   $$
   x^2 - 6x + 8
   $$

In summary, the expanded forms are:
- $$ (5a + 2)(3a - 1) = 15a^2 + a - 2 $$
- $$ (x - 4)(x - 2) = x^2 - 6x + 8 $$
The expanded forms are: - $$ (5a + 2)(3a - 1) = 15a^2 + a - 2 $$ - $$ (x - 4)(x - 2) = x^2 - 6x + 8 $$

\( \left. \begin{array} { l } { ( 5 a + 2 ) ( 3 a - 1 ) = } \\ { ( x - 4 ) ( x - 2 ) = } \end{array} \right. \)

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