Question

Упростите выражение (х-3)^2(х+3)^2СРОЧНО!!!​

Answer 1

$(x-3)^2(x+3)^2=((x-3)\cdot(x+3))^2=(x^2-9)^2=x^4-18x^2+81$

Answer 2

Simplifying the Expression (x-3)^2(x+3)^2

To simplify the expression \((x-3)^2(x+3)^2\), we can use the formula \((a-b)^2 = a^2 - 2ab + b^2\). Let's simplify step by step.

1. First, expand \((x-3)^2\): \((x-3)^2 = x^2 - 6x + 9\)

2. Next, expand \((x+3)^2\): \((x+3)^2 = x^2 + 6x + 9\)

3. Now, multiply the two expanded expressions together: \((x^2 - 6x + 9)(x^2 + 6x + 9)\)

4. Use the distributive property to multiply the expressions: \((x^2)(x^2) + (x^2)(6x) + (x^2)(9) - (6x)(x^2) - (6x)(6x) - (6x)(9) + (9)(x^2) + (9)(6x) + (9)(9)\)

5. Simplify the expression: \(x^4 + 6x^3 + 9x^2 - 6x^3 - 36x^2 - 54x + 9x^2 + 54x + 81\)

6. Combine like terms: \(x^4 + 18x^2 + 81\)

So, the simplified expression is \(x^4 + 18x^2 + 81\).

This is the simplified form of the given expression \((x-3)^2(x+3)^2\).