Name: $\newline$ Aaliyan syed $\newline$ Date: $\newline$ $3 / 26 / 24$ $\newline$ $8$ . $5$ SOLVING QUADRATICS BY COMPLETING THE SQUARE $\newline$ $1$ . Which trinomial is equivalent to $(x-8)^{2}$ ? $\newline$ ( $1$ ) $x^{2}-8 x-16$ $\newline$ ( $2$ ) $x^{2}-8 x+16$ $\newline$ ( $3$ ) $x^{2}-16 x+64$ $\newline$ ( $4$ ) $x^{2}-16 x-64$

Full solution

Q. Name:

\newline

Aaliyan syed

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Date:

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3 / 26 / 24

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8

5

SOLVING QUADRATICS BY COMPLETING THE SQUARE

\newline

1

. Which trinomial is equivalent to

(x-8)^{2}

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(

1

)

x^{2}-8 x-16

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(

2

)

x^{2}-8 x+16

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(

3

)

x^{2}-16 x+64

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(

4

)

x^{2}-16 x-64

Expand Expression: Expand the given expression $(x-8)^2$ using the formula $(a-b)^2 = a^2 - 2ab + b^2$ . Here, $a = x$ and $b = 8$ . So, $(x-8)^2 = x^2 - 2(x)(8) + 8^2$ .
Calculate Terms: Calculate the value of each term in the expanded expression. $\newline$ $x^2$ is the square of $x$ , which is $x^2$ . $\newline$ $-2(x)(8)$ is the product of $-2$ , $x$ , and $8$ , which is $-16x$ . $\newline$ $8^2$ is the square of $8$ , which is $x$ $0$ . $\newline$ So, $x$ $1$ .
Compare Options: Compare the expanded expression with the given options to find the equivalent trinomial. $\newline$ The expanded expression is $x^2 - 16x + 64$ . $\newline$ Option ( $1$ ) is $x^2 - 8x - 16$ , which does not match. $\newline$ Option ( $2$ ) is $x^2 - 8x + 16$ , which does not match. $\newline$ Option ( $3$ ) is $x^2 - 16x + 64$ , which matches the expanded expression. $\newline$ Option ( $4$ ) is $x^2 - 16x - 64$ , which does not match.
Conclude Solution: Conclude that the equivalent trinomial to $(x-8)^2$ is the one that matches the expanded expression. $\newline$ The correct option is $(3) x^2 - 16x + 64$ .