Question

a^2 + a + 1 / 4.
Q.. State whether or not the expression is a trinomial square. If it is, factorise the expressions.. ​

Answer 1

Solution :

The given expression -

a² + a + ¼ .

Yes this is a quadratic equation ( has a term with degree 2) and is a trinomial.

It can be factorised .

a² + a + ¼

>> a² + 2 × (½) × a + (½)²

>> ( a+½)²

>> (a+½)(a+½)

>> ¼[2a+1]²

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Answer 2

$\large\underline{\underline{\maltese{\red{\pmb{\sf{\: Given :-}}}}}}$

Equation :

${\bf{ {a}^{2} + a + \frac{1}{4} }}$

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$\large\underline{\underline{\maltese{\gray{\pmb{\sf{\: To \: Find :-}}}}}}$

• State weather the expression is a trinomial square. If it is a trinomial square than factorize it.

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$\large\underline{\underline{\maltese{\purple{\pmb{\sf{\: Solution :-}}}}}}$

• Yes , it is a trinomial square. Hence it can be Factorized. Degree is 2.

❒ Factorising :

$\: \: \: {:\longmapsto{\sf{a² + a + \dfrac{1}{4}}}}$

$\: \: \: {:\longmapsto{\sf{a² + 2 \times \bigg(\dfrac{1}{2}\bigg) \times a + \bigg(\dfrac{1}{2} \bigg)^2}}}$

$\: \: \: {:\longmapsto{\sf{\bigg(a + \dfrac{1}{2} \bigg) ^2}}}$

$\: \: \: \red{:\longmapsto{\underline{\boxed{\green{\sf{\dfrac{1}{4} \bigg(2a + 1\bigg)^2}}}}}}$

❒ Therefore :

❝ 1/4 (2a + 1)² is the required answer . ❞

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