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Factorise. $g^2-10g+25=0$

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Factor quadratics

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Q. Factorise.

g^2-10g+25=0

Identify Form: Identify the form of the quadratic trinomial. $\newline$ The expression $g^2 - 10g + 25$ is a quadratic trinomial in the form of $a^2 - 2ab + b^2$ .
Rewrite $a^2$ : Rewrite $g^2$ in the form of $a^2$ . $\newline$ Since $g^2$ is already in the form of $a^2$ , we have $a = g$ .
Rewrite $b^2$ : Rewrite $25$ in the form of $b^2$ . $\newline$ $25$ is a perfect square, as $5^2 = 25$ , so we have $b = 5$ .
Check Middle Term: Check the middle term $-10g$ to see if it fits the form $-2ab$ . For $a = g$ and $b = 5$ , the term $-2ab$ would be $-2 \times g \times 5 = -10g$ , which matches the middle term of the quadratic trinomial.
Write Factored Form: Write the factored form of the expression $g^2 - 10g + 25$ . Since the expression fits the form $a^2 - 2ab + b^2$ , it can be factored as $(a - b)^2$ . Substitute $a = g$ and $b = 5$ into $(a - b)^2$ to get $(g - 5)^2$ .

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