$Simplify (7 x + 4 y)^{2} + (7 x - 4 y)^{2}$

Open in App

Solution

To solve this, we need to use the following algebraic identities:

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

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

Adding the above two formulas we have:

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

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

Here we have a = 7x and b = 4y. Substituting this in the above expression we have:

$(7 x + 4 y)^{2} + (7 x - 4 y)^{2} = 2 (7 x)^{2} + 2 (4 y)^{2}$

$= 98 x^{2} + 32 y^{2}$

Suggest Corrections

Similar questions

Simplify (7 x + 4 y)^{2} + (7 x - 4 y)^{2}

I. 2 $x^{2}$ - 7x + 6 = 0
II. 4 $y^{2}$ = 9

Evaluate: $(2 y + 5) (2 y + 5)$

Using an identity expand :
$(2 y + 5) (2 y + 5)$

\frac{x^{2}}{4 y^{2}} - \frac{2}{3} + \frac{4 y^{2}}{9 x^{2}}

Join BYJU'S Learning Program