Expanding the given expression:The given expression is 27x^3+8y^3.⇒ 27x^3+8y^3=(3x)^3+(2y)^3We know identity, a^3+b^3=(a+b)(a^2 ab+b^2).Here, a=3x,b=2y.Substitu ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard VIII

Mathematics

Identity (x+a)(x+b)(x+c)

27x3+8y3=3x+2...

Question

$27 x^{3} + 8 y^{3} = (3 x + 2 y) (__)$

Open in App

Solution

Expanding the given expression:
The given expression is $27 x^{3} + 8 y^{3}$ .
$\Rightarrow 27 x^{3} + 8 y^{3} = {(3 x)}^{3} + {(2 y)}^{3}$
We know identity, $a^{3} + b^{3} = (a + b) (a^{2} - a b + b^{2})$ .
Here, $a = 3 x, b = 2 y$ .
Substituting values in the identity we have:
${(3 x)}^{3} + {(2 y)}^{3} = (3 x + 2 y) [{(3 x)}^{2} - (3 x) (2 y) + {(2 y)}^{2}] = (3 x + 2 y) (9 x^{2} - 6 x y + 4 y^{2})$
So, ${(3 x)}^{3} + {(2 y)}^{3} = (3 x + 2 y) (9 x^{2} - 6 x y + 4 y^{2})$ .

Suggest Corrections

Similar questions

If $3 x + 2 y = 9 a n d x y = 3, f i n d : 27 x^{3} + 8 y^{3}$

Q. Find the value of 27x³ + 8y³, if

(i) 3x + 2y = 14 and xy = 8

(ii) 3x + 2y = 20 and xy =

\frac{14}{9}

If $3 x + \frac{1}{3 x} = 3; f i n d : (i) 9 x^{2} + \frac{1}{9 x^{2}} (i i) 27 x^{3} + \frac{1}{27 x^{3}}$

The expanded form of $(3 x - 5)^{3}$ is
(a) $27 x^{3} + 135 x^{2} + 225 x - 125$
(b) $27 x^{3} + 135 x^{2} - 225 x - 125$
(c) $27 x^{3} - 135 x^{2} + 225 x - 125$
(d) none of these

If $3 x - 4 y = 5 a n d x y = 3, f i n d : 27 x^{3} - 64 y^{3} .$

Join BYJU'S Learning Program

27x3+8y3=(3x+2y)__

Expanding the given expression:The given expression is 27x3+8y3.⇒27x3+8y3=3x3+2y3We know identity, a3+b3=a+ba2-ab+b2.Here, a=3x,b=2y.Substituting values in the identity we have:3x3+2y3=3x+2y3x2-3x2y+2y2=3x+2y9x2-6xy+4y2So, 3x3+2y3=3x+2y9x2-6xy+4y2.

$27 x^{3} + 8 y^{3} = (3 x + 2 y) (__)$