Question

select all the correct answers.
which expressions can be factored using the difference of squares identity?
□ 49x - x⁴
□ 6x² - 81
□ x⁴ - 400
□ 32y² - 8z²
□ 4a² - 64b⁵

Explanation:

Step1: Recall difference of squares rule

A binomial $A^2 - B^2$ can be factored as $(A-B)(A+B)$. Each term must be a perfect square, and it must be a subtraction of two terms.

Step2: Analyze $49x - x^4$

Factor out $x$ first: $x(49 - x^3)$. $49 - x^3$ is a difference of cubes, not squares. Not valid.

Step3: Analyze $6x^2 - 81$

$6x^2$ is not a perfect square (6 is not a perfect square). Not valid.

Step4: Analyze $x^4 - 400$

Rewrite as $(x^2)^2 - (20)^2$, which fits $A^2-B^2$. Valid.

Step5: Analyze $32y^2 - 8z^2$

Factor out 8 first: $8(4y^2 - z^2) = 8[(2y)^2 - z^2]$, which fits the identity. Valid.

Step6: Analyze $4a^2 - 64b^5$

$64b^5$ is not a perfect square (exponent 5 is odd). Not valid.

Answer:

• $x^4 - 400$
• $32y^2 - 8z^2$