Question

factorize the expression and divide them as directed (i) (y2+7y+10) +(y+5)
(ii) (m2-14m-32) +(m+2)​

Answer 1

Answer:

I). (y+3)(y+5)

ii). (m-15)(m-2)

Step-by-step explanation:

i).

${y}^{2} + 7y + 10 + (y + 5) = {y}^{2} + 8y + 15\\ \\ = {y}^{2} + 5y + 3y + 15\\ \\ = y(y + 5) + 3(y + 5) \\ \\ = (y + 3)(y + 5)$

ii).

${m}^{2} - 14m - 32 + (m + 2) \\ \\ = {m}^{2} - 13m - 30 \\ \\ = {m}^{2} - 15m + 2m - 30 \\ \\ = m(m - 15) - 2(m - 15) \\ \\ = (m - 15)(m - 2)$

Answer 2

Step-by-step explanation:

(i) (y^2 + 7y + 10) + (y + 5)

= y^2 + 7y + 10 + y + 5

= y^2 + 8y + 15

= y^2 + 3y + 5y + 15

= y(y + 3) + 5(y + 3)

= (y + 5)(y + 3).

(ii) (m^2 - 14m - 32) + (m + 2)

= m^2 - 14m -32 + m + 2

= m^2 - 13m - 30

= m^2 - 10m + 3m - 30

= m(m - 10) + 3(m - 10)

= (m + 3)(m - 10).