We use the standard algebraic identity a² - b² = (a - b)(a + b) with a = x² and b = (y + z)². This factors the original expression into two quadratic factors.

to power 4 - (start Y + Z) close raise to power 4 and the question says factorise

Answer: $(x - y - z)(x + y + z)\left(x^2 + (y + z)^2\right)$

Step-by-step solution

Step 1: Express as difference of squares

We can rewrite each term as the square of another expression. Here, $x^4$ is rewritten as $(x^2)^2$ , and $(y + z)^4$ is rewritten as $((y + z)^2)^2$ .

Step 2: Apply identity for difference of squares

We use the standard algebraic identity $a^2 - b^2 = (a - b)(a + b)$ with $a = x^2$ and $b = (y + z)^2$ . This factors the original expression into two quadratic factors.

Step 3: Factorise the first term further

The first factor, $x^2 - (y + z)^2$ , is itself a difference of two squares. Applying the identity $a^2 - b^2 = (a - b)(a + b)$ with $a = x$ and $b = y + z$ , we get $(x - y - z)(x + y + z)$ .

Step 4: Combine all factors

We combine the factored parts together to obtain the complete factorization. Expanding or leaving the second factor as $x^2 + (y + z)^2$ gives the final factorised form.

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