Question

Factorize the following by a suitable identity & mention it.
(m2+ 7m + 10 )

Answer 1

Answer:

(m + 5)(m + 2)

Step-by-step explanation:

a² - b² = (a - b)(a + b)

(a ± b)² = a² ± 2ab + b²

~~~~~~~~

m² + 7m + 10 =

(m² + 2 × $\frac{7}{2}$ × m + $\frac{49}{4}$ ) - $\frac{49}{4}$ + 10 =

(m + $\frac{7}{2}$ )² - $(\frac{3}{2})$² = (m + $\frac{7}{2}$ + $\frac{3}{2}$ )(m + $\frac{7}{2}$ - $\frac{3}{2}$ ) =

(m + 5)(m + 2)

Answer 2

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(m + 5)(m + 2)

Step-by-step explanation:

a² - b² = (a - b)(a + b)

(a ± b)² = a² ± 2ab + b²

~~~~~~~~

m² + 7m + 10 =

(m² + 2 × \frac{7}{2}

2

7

× m + \frac{49}{4}

4

49

) - \frac{49}{4}

4

49

+ 10 =

(m + \frac{7}{2}

2

7

)² - (\frac{3}{2})(

2

3

) ² = (m + \frac{7}{2}

2

7

+ \frac{3}{2}

2

3

)(m + \frac{7}{2}

2

7

- \frac{3}{2}

2

3

) =

(m + 5)(m + 2)