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Simplify the expression: [tex]\((z-5)(z+3)\)[/tex]

Sagot :

To solve the expression [tex]\((z - 5)(z + 3)\)[/tex], we can expand it using the distributive property (also known as the FOIL method, which stands for First, Outer, Inner, Last). Here's the detailed step-by-step process:

1. First: Multiply the first terms of each binomial.
[tex]\[ z \cdot z = z^2 \][/tex]

2. Outer: Multiply the outer terms of each binomial.
[tex]\[ z \cdot 3 = 3z \][/tex]

3. Inner: Multiply the inner terms of each binomial.
[tex]\[ -5 \cdot z = -5z \][/tex]

4. Last: Multiply the last terms of each binomial.
[tex]\[ -5 \cdot 3 = -15 \][/tex]

Now, combine all these results together:
[tex]\[ z^2 + 3z - 5z - 15 \][/tex]

Next, combine like terms:
[tex]\[ z^2 + (3z - 5z) - 15 \][/tex]

Simplify the expression in the parentheses:
[tex]\[ 3z - 5z = -2z \][/tex]

So, the expanded form of [tex]\((z - 5)(z + 3)\)[/tex] is:
[tex]\[ z^2 - 2z - 15 \][/tex]

Hence, the simplified expression is also:
[tex]\[ z^2 - 2z - 15 \][/tex]

So, the final result of expanding and simplifying [tex]\((z - 5)(z + 3)\)[/tex] is:

[tex]\[ z^2 - 2z - 15 \][/tex]

This can be concluded with:
[tex]\[ (z^2 - 2z - 15, z^2 - 2z - 15) \][/tex]