Sure! Let's expand each expression step-by-step.
### Part a: Expand [tex]\( x(x - 6) \)[/tex]
1. Distribute [tex]\( x \)[/tex] to both terms inside the parentheses:
[tex]\[
x(x - 6) = x \cdot x - x \cdot 6
\][/tex]
2. Perform the multiplications:
[tex]\[
x \cdot x = x^2 \quad \text{and} \quad x \cdot 6 = 6x
\][/tex]
3. Put the terms together:
[tex]\[
x(x - 6) = x^2 - 6x
\][/tex]
### Part b: Expand [tex]\( x(4x + 1) \)[/tex]
1. Distribute [tex]\( x \)[/tex] to both terms inside the parentheses:
[tex]\[
x(4x + 1) = x \cdot 4x + x \cdot 1
\][/tex]
2. Perform the multiplications:
[tex]\[
x \cdot 4x = 4x^2 \quad \text{and} \quad x \cdot 1 = x
\][/tex]
3. Put the terms together:
[tex]\[
x(4x + 1) = 4x^2 + x
\][/tex]
### Part c: Expand [tex]\( 2x(5x + 4) \)[/tex]
1. Distribute [tex]\( 2x \)[/tex] to both terms inside the parentheses:
[tex]\[
2x(5x + 4) = 2x \cdot 5x + 2x \cdot 4
\][/tex]
2. Perform the multiplications:
[tex]\[
2x \cdot 5x = 10x^2 \quad \text{and} \quad 2x \cdot 4 = 8x
\][/tex]
3. Put the terms together:
[tex]\[
2x(5x + 4) = 10x^2 + 8x
\][/tex]
### Part d: Expand [tex]\( 3x(5x - y) \)[/tex]
1. Distribute [tex]\( 3x \)[/tex] to both terms inside the parentheses:
[tex]\[
3x(5x - y) = 3x \cdot 5x + 3x \cdot (-y)
\][/tex]
2. Perform the multiplications:
[tex]\[
3x \cdot 5x = 15x^2 \quad \text{and} \quad 3x \cdot (-y) = -3xy
\][/tex]
3. Put the terms together:
[tex]\[
3x(5x - y) = 15x^2 - 3xy
\][/tex]
So the expanded forms are:
- a) [tex]\( x(x - 6) = x^2 - 6x \)[/tex]
- b) [tex]\( x(4x + 1) = 4x^2 + x \)[/tex]
- c) [tex]\( 2x(5x + 4) = 10x^2 + 8x \)[/tex]
- d) [tex]\( 3x(5x - y) = 15x^2 - 3xy \)[/tex]
