Applying the identity a² - b² = (a - b)(a + b) with a = x² and b = (x - z)², we factor the expression into two factors.

The first factor x² - (x - z)² is itself a difference of squares. Using a² - b² = (a - b)(a + b) with a = x and b = x - z, we get [x - (x - z)][x + (x - z)] = z(2x - z).

Now expand the second factor using the identity (x - z)² = x² - 2xz + z² and combine the like terms x² + x² = 2x².

x raise to power 4 -(x-z)raise to power 4 . Factorise

Answer: $z(2x - z)(2x^2 - 2xz + z^2)$

Step-by-step solution

Step 1: Express as difference of squares

We rewrite each term as the square of another expression to apply the difference of squares identity, $a^2 - b^2 = (a - b)(a + b)$ . Here, $a = x^2$ and $b = (x - z)^2$ .

Step 2: Apply difference of squares identity

Applying the identity $a^2 - b^2 = (a - b)(a + b)$ with $a = x^2$ and $b = (x - z)^2$ , we factor the expression into two factors.

Step 3: Factor the first bracket

The first factor $x^2 - (x - z)^2$ is itself a difference of squares. Using $a^2 - b^2 = (a - b)(a + b)$ with $a = x$ and $b = x - z$ , we get $[x - (x - z)][x + (x - z)] = z(2x - z)$ .

Step 4: Expand and simplify the second bracket

Now expand the second factor using the identity $(x - z)^2 = x^2 - 2xz + z^2$ and combine the like terms $x^2 + x^2 = 2x^2$ .

Step 5: Combine all factors

Combining the simplified factors together, we obtain the complete factorised form of the expression.

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