How do you multiply #(x - 2) ( x ^ { 2} - 7x + 4)#?

Question

Avery Alexander · Accepted Answer

See the entire solution process below:

You multiply each term in the left parenthesis by each term in the right parenthesis to get the product of these two terms. #(color(red)(x) - color(red)(2))(color(blue)(x^2) - color(blue)(7x) + color(blue)(4))# becomes: #(color(red)(x) xx color(blue)(x^2)) - (color(red)(x) xx color(blue)(7x)) + (color(red)(x) xx color(blue)(4)) - (color(red)(2) xx color(blue)(x^2)) + (color(red)(2) xx color(blue)(7x)) - (color(red)(2) xx color(blue)(4))# #x^3 - 7x^2 + 4x - 2x^2 + 14x - 8# Now, we are able to combine and group like terms: #x^3 - 7x^2 - 2x^2 + 4x + 14x - 8# #x^3 + (-7 - 2)x^2 + (4 + 14)x - 8# #x^2 - 9x^2 + 18x - 8#

Julia Adams · Answer

undefined To multiply $(x - 2)(x^2 - 7x + 4)$, you can use the distributive property or the FOIL method:

Using the distributive property:

$$ (x - 2)(x^2 - 7x + 4) = x(x^2 - 7x + 4) - 2(x^2 - 7x + 4) $$

$$ = x^3 - 7x^2 + 4x - 2x^2 + 14x - 8 $$

$$ = x^3 - 9x^2 + 18x - 8 $$

Alternatively, you can use the FOIL method (First, Outer, Inner, Last):

$$ (x - 2)(x^2 - 7x + 4) $$

$$ = x \cdot x^2 - x \cdot 7x + x \cdot 4 - 2 \cdot x^2 + (-2) \cdot (-7x) + (-2) \cdot 4 $$

$$ = x^3 - 7x^2 + 4x - 2x^2 + 14x - 8 $$

$$ = x^3 - 9x^2 + 18x - 8 $$

So, the product of $(x - 2)(x^2 - 7x + 4)$ is $x^3 - 9x^2 + 18x - 8$.