Factorise: (3x – 4y)⁴ – x⁴

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Recognize as difference of squares: Recognize the expression as a difference of two squares. The given expression is a difference of two squares because it can be written as A⁴ - B⁴, where A = (3x - 4y) and B = x.Apply formula: Apply the difference of squares formula. The difference of squares formula is A² - B² = (A - B)(A + B). In this case, we can apply the formula to A² and B², where A² = (3x - 4y)² and B² = x².Write as difference of squares: Write the expression as a difference of squares. Using the formula from Step 2, we can write the expression as: ((3x - 4y)²)² - (x²)² = ((3x - 4y)² - x²)((3x - 4y)² + x²)Expand terms: Expand the terms inside the parentheses. We need to expand (3x - 4y)² and x²: (3x - 4y)² = 9x² - 24xy + 16y² (by squaring each term and applying the distributive property) x² = x² (no expansion needed)Substitute expanded terms: Substitute the expanded terms back into the factored form. Substitute the expanded form of (3x - 4y)² into the factored expression from Step 3: (9x² - 24xy + 16y² - x²)(9x² - 24xy + 16y² + x²)Combine like terms: Combine like terms in each factor. In the first factor, combine 9x² and -x² to get 8x². In the second factor, combine 9x² and x² to get 10x²: (8x² - 24xy + 16y²)(10x² - 24xy + 16y²)Check for further factorization: Check for any further factorization. The terms within each factor do not have a common factor, and the expression cannot be factored further.

Factorise: $\newline$ $(3x - 4y)^4 - x^4$

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Factorise:\newline(3x−4y)4−x4(3x - 4y)^4 - x^4(3x−4y)4−x4

Factorise: $\newline$ $(3x - 4y)^4 - x^4$