Question

factorise 2y^2+15y+25=೦​

Answer 1

♣ɢɪᴠᴇɴ:–

$\large\tt{2y^2+15y+25=೦}$

♣ᴛᴏ ғɪɴᴅ:–

• Factorise.

♣sᴏʟᴜᴛɪᴏɴ:–

First write the given equation

$\qquad\quad {:}\leadsto\tt 2y^2+15y+25=0$

Now use mid term factorisation

We need to find two numbers by which if we multiply the product is 50 and the sum of them is 15

The numbers are 10 and 5

• 10×5=50
• 10+5=15

$\qquad\quad {:}\leadsto\tt 2y^2+10y+5y+25=0$

Take common multiple

$\qquad\quad {:}\leadsto\tt 2y (y+5)+5 (y+5)=0$

$\qquad\quad {:}\leadsto\tt (y+5)(2y+5)=0$

$\qquad\quad{:}\leadsto\tt(y+5)=0\quad or\quad (2y+5)=0$

Interchange sides in Equations

$\qquad\quad {:}\leadsto\tt y=-5 \quad or \quad y=\dfrac {-5}{2}$

$\therefore{\boxed{\color {emerald}{\sf y=-5\:or\:\dfrac {-5}{2}}}}$

Answer 2

♣ɢɪᴠᴇɴ:–

$\large\tt{2y^2+15y+25=೦}$

♣ᴛᴏ ғɪɴᴅ:–

Factorise.

♣sᴏʟᴜᴛɪᴏɴ:–

First write the given equation

$\qquad\quad {:}\leadsto\tt 2y^2+15y+25=0$

Now use mid term factorisation

We need to find two numbers by which if we multiply the product is 50 and the sum of them is 15

The numbers are 10 and 5

10×5=50

10+5=15

$\qquad\quad {:}\leadsto\tt 2y^2+10y+5y+25=0$

Take common multiple

$\qquad\quad {:}\leadsto\tt 2y (y+5)+5 (y+5)=0$

$\qquad\quad {:}\leadsto\tt (y+5)(2y+5)=0$

$\qquad\quad{:}\leadsto\tt(y+5)=0\quad or\quad (2y+5)=0$

Interchange sides in Equations

$\qquad\quad {:}\leadsto\tt y=-5 \quad or \quad y=\dfrac {-5}{2}$

$\therefore{\boxed{\color {emerald}{\sf y=-5\:or\:\dfrac {-5}{2}}}}$