The expresssion x4 - 4 can be factorized as x2 -2x- 2 x2 -2x -2x2 - 2x- 2 x2 -2x -2 x2 - 2x- 2 x2 -2x- 2x2 -2 x2 -2

The correct option is B (x^2 + 2x+ 2) ( x^2 2x +2) x^4 + 4 = x^4 + 4 + 4x^2 4x^2 = (x^2 )^2 + (2)^2 + 2 × x^2 × 2 (2x)^2 = (x^2 + 2)^2 (2x)^2 ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard IX

Mathematics

Algebraic Identities

The expresssi...

Question

The expresssion $x^{4} + 4$ can be factorized as

$(x^{2} + 2 x + 2) (x^{2} - 2 x + 2)$

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

$(x^{2} + 2 x + 2) (x^{2} + 2 x - 2)$

No worries! We‘ve got your back. Try BYJU‘S free classes today!

$(x^{2} - 2 x - 2) (x^{2} - 2 x + 2)$

No worries! We‘ve got your back. Try BYJU‘S free classes today!

$(x^{2} + 2) (x^{2} - 2)$

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A
$(x^{2} + 2 x + 2) (x^{2} - 2 x + 2)$

$x^{4} + 4 = x^{4} + 4 + 4 x^{2} - 4 x^{2} = (x^{2})^{2} + (2)^{2} + 2 \times x^{2} \times 2 - (2 x)^{2} = (x^{2} + 2)^{2} - (2 x)^{2} (x^{2} + 2 + 2 x) (x^{2} + 2 - 2 x) = (x^{2} + 2 x + 2) (x^{2} - 2 x + 2)$

Suggest Corrections

Similar questions

Q. The expression x⁴ + 4 can be factorized as

(a) (x² + 2x + 2) (x² − 2x + 2)

(b) (x² + 2x + 2) (x² + 2x + 2)

(c) (x² − 2x − 2) (x²− 2x + 2)

(d) (x² + 2) (x² − 2)

Subtract: 2 x^{2} + 6 - 4 x from 3 x^{2} - 6 x + 8.

Q. Subtracting

2 x^{2} + 6 - 4 x

from

3 x^{2} - 6 x + 8

gives .

${lim}_{x \to \sqrt{2}} \frac{x^{2} - 2}{x^{2} + \sqrt{2 x} - 4}$

Question 2
Which of the following is not a quadratic equation?
(a) $2 (x - 1)^{2} = 4 x^{2} - 2 x + 1$
(b) $2 x - x^{2} = x^{2} + 5$
(c) ${(\sqrt{2} x + \sqrt{3})}^{2} = 3 x^{2} - 5 x$
(d) $(x^{2} + 2 x)^{2} = x^{4} + 3 + 4 x^{3}$

Join BYJU'S Learning Program

The expresssion x4+4 can be factorized as

The correct option is A (x2+2x+2)(x2−2x+2) x4+4=x4+4+4x2−4x2=(x2)2+(2)2+2×x2×2−(2x)2=(x2+2)2−(2x)2(x2+2+2x)(x2+2−2x)=(x2+2x+2)(x2−2x+2)

The expresssion $x^{4} + 4$ can be factorized as

The correct option is A
$(x^{2} + 2 x + 2) (x^{2} - 2 x + 2)$

$x^{4} + 4 = x^{4} + 4 + 4 x^{2} - 4 x^{2} = (x^{2})^{2} + (2)^{2} + 2 \times x^{2} \times 2 - (2 x)^{2} = (x^{2} + 2)^{2} - (2 x)^{2} (x^{2} + 2 + 2 x) (x^{2} + 2 - 2 x) = (x^{2} + 2 x + 2) (x^{2} - 2 x + 2)$