How do you multiply ${(3 x - 1)}^{2}$ $(3x- 1)^2$ ?

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How do you multiply ${(3 x - 1)}^{2}$ $(3x- 1)^2$ ?

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Answer 1 · 2017-07-24T11:20:48

See a solution process below:

Explanation:

Use this rule to multiply this expression:

${(a - b)}^{2} = a^{2} - 2 a b + b^{2}$ $(color(red)(a) - color(blue)(b))^2 = color(red)(a)^2 - 2color(red)(a)color(blue)(b) + color(blue)(b)^2$

Substituting $3 x$ $3x$ for $a$ $a$ and $1$ $1$ for $b$ $b$ gives:

${((3 x) - 1)}^{2} \Rightarrow {(3 x)}^{2} - (2 \cdot 3 x \cdot 1) + 1^{2} \Rightarrow$ $(color(red)((3x)) - color(blue)(1))^2 => color(red)((3x))^2 - (2 * color(red)(3x) * color(blue)(1)) + color(blue)(1)^2 =>$

$9 x^{2} - 6 x + 1$ $9x^2 - 6x + 1$

Another method is to first rewrite the expression as:

$(3 x - 1) (3 x - 1)$ $(3x - 1)(3x - 1)$

To multiply these two terms you multiply each individual term in the left parenthesis by each individual term in the right parenthesis.

$(3 x - 1) (3 x - 1)$ $(color(red)(3x) - color(red)(1))(color(blue)(3x) - color(blue)(1))$ becomes:

$(3 x \times 3 x) - (3 x \times 1) - (1 \times 3 x) + (1 \times 1)$ $(color(red)(3x) xx color(blue)(3x)) - (color(red)(3x) xx color(blue)(1)) - (color(red)(1) xx color(blue)(3x)) + (color(red)(1) xx color(blue)(1))$

$9 x^{2} - 3 x - 3 x + 1$ $9x^2 - 3x - 3x + 1$

We can now combine like terms:

$9 x^{2} + (- 3 - 3) x + 1$ $9x^2 + (-3 - 3)x + 1$

$9 x^{2} + (- 6) x + 1$ $9x^2 + (-6)x + 1$

$9 x^{2} - 6 x + 1$ $9x^2 - 6x + 1$

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How do you multiply ${(3 x - 1)}^{2}$ $(3x- 1)^2$ ?

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