Question

A) (x+3)(x² - 3x + 9); ​

Answer 1

Покрокове пояснення:

Спростіть добуток за формулою:

$(a+b)(a^{2} -ab+b^{2} )=a^{3} +b^{3}\\x^{3}+3^{3} \\x^{3}+27$

Answer 2

To multiply the two expressions $(x + 3)$ and $(x^2 - 3x + 9)$, you can use the distributive property. Here's how you can do it step by step:

$(x + 3)(x^2 - 3x + 9)$

First, distribute the first term, $x$, into the second expression:

$x \cdot x^2 - x \cdot 3x + x \cdot 9$

This simplifies to:

$x^3 - 3x^2 + 9x$

Now, distribute the second term, $3$, into the second expression:

$3 \cdot x^2 - 3 \cdot 3x + 3 \cdot 9$

This simplifies to:

$3x^2 - 9x + 27$

Now, you have two expressions:

$x^3 - 3x^2 + 9x$ and $3x^2 - 9x + 27$

Finally, add these two expressions together:

$(x^3 - 3x^2 + 9x) + (3x^2 - 9x + 27)$

Now, combine like terms:

$x^3 - 3x^2 + 3x^2 - 9x - 9x + 9x + 27$

The middle terms cancel each other out, and you're left with:

$x^3 + 27$

So, $(x + 3)(x^2 - 3x + 9)$ simplifies to $x^3 + 27$.