Solved on Feb 21, 2024

Rewrite the product $(x+3)(x-3)$ as a difference of two squares.

STEP 1

Assumptions
1. We are given the product $(x+3)(x-3)$ .
2. We need to express this product as a difference of two squares.

STEP 2

Recall the algebraic identity for the difference of two squares:
$a^2 - b^2 = (a+b)(a-b)$

STEP 3

Identify $a$ and $b$ in the given expression such that $(x+3)$ corresponds to $(a+b)$ and $(x-3)$ corresponds to $(a-b)$ .

STEP 4

From the structure of the given expression, we can see that $a = x$ and $b = 3$ .

STEP 5

Now, apply the identity for the difference of two squares using the identified values of $a$ and $b$ .
$a^2 - b^2 = (a+b)(a-b)$
$x^2 - 3^2 = (x+3)(x-3)$

STEP 6

Calculate the squares of $a$ and $b$ .
$x^2 - 3^2 = x^2 - 9$

STEP 7

Thus, the product $(x+3)(x-3)$ is expressed as the difference of two squares:
$x^2 - 9$
The product as a difference of two squares is $x^2 - 9$ .

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Rewrite the product $(x+3)(x-3)$ as a difference of two squares.

STEP 1

Assumptions
1. We are given the product $(x+3)(x-3)$ .
2. We need to express this product as a difference of two squares.

STEP 2

Recall the algebraic identity for the difference of two squares:
$a^2 - b^2 = (a+b)(a-b)$

STEP 3

Identify $a$ and $b$ in the given expression such that $(x+3)$ corresponds to $(a+b)$ and $(x-3)$ corresponds to $(a-b)$ .

STEP 4

From the structure of the given expression, we can see that $a = x$ and $b = 3$ .

STEP 5

Now, apply the identity for the difference of two squares using the identified values of $a$ and $b$ .
$a^2 - b^2 = (a+b)(a-b)$
$x^2 - 3^2 = (x+3)(x-3)$

STEP 6

Calculate the squares of $a$ and $b$ .
$x^2 - 3^2 = x^2 - 9$

STEP 7

Thus, the product $(x+3)(x-3)$ is expressed as the difference of two squares:
$x^2 - 9$
The product as a difference of two squares is $x^2 - 9$ .

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Rewrite the product (x+3)(x−3)(x+3)(x-3)(x+3)(x−3) as a difference of two squares.

STEP 1

Assumptions1. We are given the product (x+3)(x−3)(x+3)(x-3)(x+3)(x−3).2. We need to express this product as a difference of two squares.

STEP 2

Recall the algebraic identity for the difference of two squares:a2−b2=(a+b)(a−b)a^2 - b^2 = (a+b)(a-b)a2−b2=(a+b)(a−b)

STEP 3

Identify aaa and bbb in the given expression such that (x+3)(x+3)(x+3) corresponds to (a+b)(a+b)(a+b) and (x−3)(x-3)(x−3) corresponds to (a−b)(a-b)(a−b).

STEP 4

From the structure of the given expression, we can see that a=xa = xa=x and b=3b = 3b=3.

STEP 5

Now, apply the identity for the difference of two squares using the identified values of aaa and bbb.a2−b2=(a+b)(a−b)a^2 - b^2 = (a+b)(a-b)a2−b2=(a+b)(a−b)x2−32=(x+3)(x−3)x^2 - 3^2 = (x+3)(x-3)x2−32=(x+3)(x−3)

STEP 6

Calculate the squares of aaa and bbb.x2−32=x2−9x^2 - 3^2 = x^2 - 9x2−32=x2−9

STEP 7

Thus, the product (x+3)(x−3)(x+3)(x-3)(x+3)(x−3) is expressed as the difference of two squares:x2−9x^2 - 9x2−9The product as a difference of two squares is x2−9x^2 - 9x2−9.

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Rewrite the product $(x+3)(x-3)$ as a difference of two squares.

Assumptions
1. We are given the product $(x+3)(x-3)$ .
2. We need to express this product as a difference of two squares.

Recall the algebraic identity for the difference of two squares:
$a^2 - b^2 = (a+b)(a-b)$

Identify $a$ and $b$ in the given expression such that $(x+3)$ corresponds to $(a+b)$ and $(x-3)$ corresponds to $(a-b)$ .

From the structure of the given expression, we can see that $a = x$ and $b = 3$ .

Now, apply the identity for the difference of two squares using the identified values of $a$ and $b$ .
$a^2 - b^2 = (a+b)(a-b)$
$x^2 - 3^2 = (x+3)(x-3)$

Calculate the squares of $a$ and $b$ .
$x^2 - 3^2 = x^2 - 9$

Thus, the product $(x+3)(x-3)$ is expressed as the difference of two squares:
$x^2 - 9$
The product as a difference of two squares is $x^2 - 9$ .