Question

Which expression does not factor? m3 + 1 m3 – 1 m2 + 1 m2 – 1

Answer 1

Answer:

Option C. is the right option

Step-by-step explanation:

In this question we will take each option and try to factorize them.

Option A.

(m³ + 1) = (m + 1)(m² + 1² - 1.m) = (m + 1).(m² - m + 1)

[ since (a³ + b³) = (a + b).(a² + b² - ab)]

So can be factored.

Option B.

(m³ - 1) = (m - 1).(m² + m + 1)

[ since a3 + b³= (m - 1)(m² + m + 1)

So expression can be factored.

Option C.

(m² + 1) This expression is in the factored form.

Option D.

(m² - 1) = (m + 1)(m - 1)

[(a² - b²) = (a - b)(a + b)]

So expression can be factored.

Finally the answer is Option C.

Answer 2

Answer:

$m^2 +1$

Explanation:

All the other expressions can be factorized. Let's see why:

1) $m^3 +1$

This is the sum of the cubes, and this can be factorized as follows:

$a^3+b^3=(a+b)(a^2-ab+b^2)$

In this case, a=m and b=1, so we can factorize as

$m^3+1=(m+1)(m^2-m+1)$

2) $m^3-1$

This is the difference between two cubes, and this can be factorized as follows:

$a^3-b^3=(a-b)(a^2+ab+b^2)$

In this case, a=m and b=1, so we can factorize as

$m^3-1=(m-1)(m^2+m+1)$

3) $m^2-1$

This is the difference between two square numbers, and it can be factorized as follows

$(a^2-b^2)=(a+b)(a-b)$

In this case, a=m and b=1, so we can factorize as

$m^2-1=(m+1)(m-1)$