Factorize- m 4-256A- m -4 m -4 m 2-162B- m -4 m -4 m 2-16C- m-4m-4m2-16D- m -4 m -4 m 2-16

The correct option is B (m 4)(m+4) (m2 +16) m^4 256 = (m^2)^2 – (16)^2 = (m^2 – 16) (m^2 +16) Now, (m^2 +16) cannot be factorized further, but (m^2 – ...

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Standard VII

Mathematics

(a-b)^2 Expansion and Visualisation

Factorize: m ...

Question

Factorize: $m^{4} - 256.$

(m-4)(m+4) (m² +16)

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(m-4)(m+4) (m² -16)

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(m-4)(m-4) (m² +16²)

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(m+4)(m+4) (m² +16)

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Solution

The correct option is A
(m-4)(m+4) (m² +16)

$m^{4} - 256 = (m^{2})^{2} - (16)^{2}$

$= (m^{2} - 16) (m^{2} + 16)$

Now, $(m^{2} + 16)$ cannot be factorized further, but $(m^{2} - 16)$ is factorizable again.

$(m^{2} - 16) = (m)^{2} - (4)^{2} = (m - 4) (m + 4)$

Therefore, $(m^{4} - 256) = (m - 4) (m + 4) (m^{2} + 16)$ .

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Similar questions

Factorise : m^{4} - 256

Match the following:

A		B
1)	(m + 2n) (m − 2n)	a)	m² − 16
2)	(3m + n) (3m − n)	b)	4m² − 25n²
3)	(m + 4) (m − 4)	c)	4m² + 25n²
4)	(2m + 5n) (2m − 5n)	d)	m² − 4n²
		e)	9m² + n²
		f)	9m² − n²

Q. State whether True or False.

Multiply:

2 m^{2} - 3 m - 1

and

4 m^{2} - m - 1

The answer is

8 m^{4} - 14 m^{3} - 3 m^{2} + 4 m + 1

Find the third side of a triangle whose two sides are $(3 m^{2} - 5 m$ ) and $(4 m^{2} + 12$ ) and perimeter is $(8 m^{2} - 9 m + 4$ ).

Find the third side of a triangle whose perimeter is $8 m^{2} - 9 m + 4$ and two of its sides are $3 m^{2} - 5 m$ and $4 m^{2} + 12$ .

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Factorize: m4−256.

The correct option is A (m-4)(m+4) (m2 +16) m4−256=(m2)2–(16)2 =(m2–16)(m2+16) Now, (m2+16) cannot be factorized further, but (m2–16) is factorizable again. (m2–16)=(m)2–(4)2=(m−4)(m+4) Therefore, (m4−256)=(m−4)(m+4)(m2+16).

Factorize: $m^{4} - 256.$