Which of the following identities is not applicable to simplify ${(8 x + 10 y)}^{2}$ - ${(10 x + 8 y)}^{2}$ ?

{(a - b)}^{2} = a^{2} - 2 a b + b^{2}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

{(a + b)}^{2} = a^{2} + 2 a b + b^{2}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

a^{2} - b^{2} = (a + b) (a - b)

No worries! We‘ve got your back. Try BYJU‘S free classes today!

All the above

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A ${(a - b)}^{2} = a^{2} - 2 a b + b^{2}$
${(8 x + 10 y)}^{2} = {(8 x)}^{2} + 2 \times (8 x) \times (10 y) \times (10 y)^{2}$
Using Identity ${(a + b)}^{2} = a^{2} + 2 a b + b^{2}$
${(8 x + 10 y)}^{2} = 64 x^{2} + 160 x y + 100 y^{2}$
${(10 x + 8 y)}^{2} = 100 x^{2} + 160 x y + 64 y^{2}$
Now ${(8 x + 10 y)}^{2} - {(10 x + 8 y)}^{2} = (64 x^{2} + 160 x y + 100 y^{2}) - (100 x^{2} + 160 x y + 64 y^{2}$ )
$= 64 x^{2} + 160 x y + 100 y^{2} - 100 x^{2} - 160 x y - 64 y^{2}$
$= 36 y^{2} - 36 x^{2}$
OR
Using Identity $a^{2} - b^{2} = (a + b) (a - b)$
${(8 x - 10 y)}^{2}) - {(10 x + 8 y)}^{2} = [(8 x + 10 y) - (10 x + 8 y)] \times [(8 x + 10 y) + (10 x + 8 y)]$
$= (y - x) (36 x + 36 y)$
$= 36 x y - 36 x^{2} + 36 y^{2} - 36 x y$
$= 36 y^{2} - 36 x^{2}$

Suggest Corrections

Similar questions

Which of the following identity is applicable to simplify (4x + 5y)^2 - (5x + 4y)^2 ?

Which of the following identity is not applicable to simplify ${(4 x + 5 y)}^{2} - {(5 x + 4 y)}^{2}$ ?

{(10 x - 1)}^{2}

{(x - 8 y)}^{2}

10 y^{2} = (x + 2) (x - 2)

Which of the following is not applicable to enantiomers?

Join BYJU'S Learning Program