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Simplify (x2 - 5)(x + 5) + 25.

Mathematics

ScanSolve AI Answer

Answer

x3+5x2−5xx^3 + 5x^2 - 5x

Step-by-step solution

3 steps

Here is the solution for question 3 (i):

3. Simplify.

  • 3 (i): (x2−5)(x+5)+25(x^2 - 5)(x + 5) + 25

  1. Multiply the binomials (x2−5)(x^2 - 5) and (x+5)(x + 5) using the distributive property (FOIL method).

    $$
(x^2 - 5)(x + 5) = x^2(x) + x^2(5) - 5(x) - 5(5)
$$
$$
= x^3 + 5x^2 - 5x - 25
$$

  2. Add the constant 25 to the result from Step 1.

    $$
x^3 + 5x^2 - 5x - 25 + 25
$$

  3. Combine the constant terms.

    $$
= \boxed{x^3 + 5x^2 - 5x}
$$
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