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Factorise the following expressions. (i)...

Factorise the following expressions. (i) `a^2+8x+16` (ii) `p^2-10p+25` (iii) `25m^2+30m+9` (iv) `49y^2+84yz+36z^2` (v) `4x^2-8x+4` (vi) `121b^2-88bc+16c^2` (vii) `(l+m)^2-4lm` (Hint : Expand `(l+m)^2}` first (viii) `a^4+2a^2 b^2 +b^4`

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Let's solve the given expressions step by step. ### (i) Factorise `a^2 + 8x + 16` 1. **Identify the quadratic form**: The expression is in the form \( a^2 + bx + c \). 2. **Find two numbers that multiply to 16 and add to 8**: The numbers are 4 and 4. 3. **Rewrite the expression**: \( a^2 + 4x + 4x + 16 \). 4. **Group the terms**: \( (a^2 + 4x) + (4x + 16) \). ...
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