Write the following cube in expanded form: $(3a + 5b)^3$.
(N/A) To expand $(3a + 5b)^3$,we use the algebraic identity $(x + y)^3 = x^3 + y^3 + 3xy(x + y)$.
Here,$x = 3a$ and $y = 5b$.
Substituting these values into the identity:
$(3a + 5b)^3 = (3a)^3 + (5b)^3 + 3(3a)(5b)(3a + 5b)$
$= 27a^3 + 125b^3 + 45ab(3a + 5b)$
$= 27a^3 + 125b^3 + 135a^2b + 225ab^2$.
Here,$x = 3a$ and $y = 5b$.
Substituting these values into the identity:
$(3a + 5b)^3 = (3a)^3 + (5b)^3 + 3(3a)(5b)(3a + 5b)$
$= 27a^3 + 125b^3 + 45ab(3a + 5b)$
$= 27a^3 + 125b^3 + 135a^2b + 225ab^2$.
Explore More
Similar Questions
Which of the following expressions is a polynomial? State the reason. If an expression is a polynomial,state whether it is a polynomial in one variable or not: $\sqrt{3} x^{2}+\pi x-9$
Easy
View SolutionExpand $(3x + 5)^2$.
Easy
View SolutionWrite the coefficient of $x^{2}$ in each of the following:
$(i)$ $\frac{\pi}{6} x + x^{2} - 1$
$(ii)$ $3x - 5$
$(i)$ $\frac{\pi}{6} x + x^{2} - 1$
$(ii)$ $3x - 5$
Easy
View SolutionIf $x-2$ is a factor of $x^{3}-3x^{2}+ax+24$,then $a = \ldots$
Easy
View SolutionWrite the following cube in expanded form:
$(7x - 4y)^{3}$
$(7x - 4y)^{3}$
Easy
View SolutionVedclass Products
For Students
Vedclass Test Series
Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.
Start Free TrialFor Teachers
Exam Paper Generator
Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.
Try FreeFor Institutes
Online Exam Module
Live online exams with unlimited students, 360° analytics & white-label branding.
See Demo