Answer :

We will use completing the square method for factorizing the expression.

We have, x^{4} + x^{2} + 25

Now we can write above expression as, (x^{2})^{2} + x^{2} + (5)^{2}

We need to make the middle term of the expression such that,

x^{2} = 2 × x^{2} × 5

x^{2} = 10 x^{2}

So, adding and subtracting 9 x^{2} from the expression,

x^{4} + x^{2} + 25 = (x^{2})^{2} + x^{2} + (5)^{2} + 9 x^{2} – 9 x^{2}

x^{4} + x^{2} + 25 = (x^{2})^{2} + 10 x^{2} + (5)^{2} – 9 x^{2}

x^{4} + x^{2} + 25 = (x^{2} + 5)^{2} – 9 x^{2}

[ Applying formula: (a + b)^{2} = a^{2} + b^{2} + 2 a b]

x^{4} + x^{2} + 25 = (x^{2} + 5)^{2} – (3 x)^{2}

Now we will apply the formula,

a^{2} – b^{2} = (a + b)(a – b)

x^{4} + x^{2} + 25 = (x^{2} + 5 + 3 x)(x^{2} +5 – 3x)

Rate this question :

Fill in the blanks to make the statements true:

On simplification = …….. .

NCERT - Mathematics ExemplarResolve each of the following quadratic trinomials into factors:

6x^{2} – 13xy + 2y^{2}

Resolve each of the following quadratic trinomials into factors:

RD Sharma - Mathematics

Resolve each of the following quadratic trinomials into factors:

RD Sharma - Mathematics

Resolve each of the following quadratic trinomials into factors:

RD Sharma - Mathematics