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

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: - \( (5a + 2)(3a - 1) = 15a^2 + a - 2 \) - \( (x - 4)(x - 2) = x^2 - 6x + 8 \)