How do you expand: ${(4 x + 5)}^{2}$ $(4x + 5)^2$ ?

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Answer 1 · 2017-11-14T01:18:19

See a solution process below;

The question is: What is ${(4 x + 5)}^{2}$ $(4x + 5)^2$

We can use this rule for quadratics:

${(x + y)}^{2} = x^{2} + 2 x y + y^{2}$ $(color(red)(x) + color(blue)(y))^2 = color(red)(x)^2 + 2color(red)(x)color(blue)(y) + color(blue)(y)^2$

Let $x = 4 x$ $x = 4x$ and let $y = 5$ $y = 5$

Substituting gives:

${(4 \times + 5)}^{2} \Rightarrow$ $(color(red)( 4xx) + color(blue)(5))^2 =>$

${(4 x)}^{2} + (2 \cdot 4 x \cdot 5) + 5^{2} \Rightarrow$ $color(red)(( 4x))^2 + (2 * color(red)( 4x) * color(blue)(5)) + color(blue)(5)^2 =>$

$16 x^{2} + 40 x + 25$ $16x^2 + 40x + 25$

How do you expand: (4x + 5)^2(4x+5)2(4x + 5)^2?