Question

Factorise the expressions by splitting the middle term
a2 - 10a + 21​

Answer 1

Concept:-

Here, We have to factorise the expression by the method of the middle term splitting.

$\sf{Expression = a^{2} - 10a + 21}$

Solution:-

Let's start our factorisation,

⇒ $\sf{a^{2} - 10a + 21}$  

⇒ $\sf{a^{2} - 7a - 3a + 21}$                              $\begin{array}{c|c} \underline{\sf {3}}&\underline{\sf { \: \: \: 21 \: \: \: }} \\ \underline{\sf {}}&\underline{\sf {\; \; 7\; \; \: }}\end{array}$

⇒ $\sf{a(a - 7) - 3(a - 7)}$

⇒ $\sf{(a - 7) (a - 3)}$

$\sf{Hence,\ The\ factorisation\ of\ expression\ a^{2} - 10a + 21\ is \ \underline{\boxed{(a-7) (a-3).}}}$

Some important terms:-

Factorization $\longrightarrow$ Factorization is defined as breaking or decomposition of an entity into a product of other entity, or factors, which when multiplied together give the original number.