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One possible way to solve this problem is by using the distributive property. You can multiply each term inside the parentheses by the term outside the parentheses.
Let’s start with the first equation:
(5x + 4) * (3x – 1)
To apply the distributive property, we multiply the first term inside the parentheses (5x) by both terms outside the parentheses (3x and -1) and then multiply the second term inside the parentheses (4) by both terms outside the parentheses:
(5x * 3x) + (5x * -1) + (4 * 3x) + (4 * -1)
Simplifying this expression gives us:
(15x^2) – 5x + (12x) – 4
Combining like terms results in:
15x^2 + 7x – 4
So the expanded form of (5x + 4) * (3x – 1) is 15x^2 + 7x – 4.
For the second equation, (3x – 2) * (2x + 1), we follow the same steps:
(3x * 2x) + (3x * 1) + (-2 * 2x) + (-2 * 1)
6x^2 + 3x – 4x – 2
Combining like terms results in:
6x^2 – x – 2
So the expanded form of (3x – 2) * (2x + 1) is 6x^2 – x – 2.
Therefore, the expanded forms of both equations are:
(5x + 4) * (3x – 1) = 15x^2 + 7x – 4
(3x – 2) * (2x + 1) = 6x^2 – x – 2
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