Download App

Factorisation of Algebraic Expressions — Maths STD 8 — Question

Maharashtra BoardEnglish MediumSTD 8MathsFactorisation of Algebraic Expressions3 Marks
Question
Factorise: $1+\frac{\mathrm{q}^3}{125}$
✓

Answer

$\begin{aligned} & \text { } 1+\frac{\mathrm{q}^3}{125} \\ & =1^3+\left(\frac{\mathrm{q}}{5}\right)^3 \\ & \text { Here, } a=1 \text { and } b=\frac{q}{5} \\ & \therefore \quad 1+\frac{\mathrm{q}^3}{125}=\left(1+\frac{\mathrm{q}}{5}\right)\left[1^2-1\left(\frac{\mathrm{q}}{5}\right)+\left(\frac{\mathrm{q}}{5}\right)^2\right] \\ & \ldots\left[\because a^3+b^3=(a+b)\left(a^2-a b+b^2\right)\right] \\ & =\left(1+\frac{q}{5}\right)\left(1-\frac{q}{5}+\frac{q^2}{25}\right) \\ & \end{aligned}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "3 Mark Question" from Factorisation of Algebraic Expressions→Factorisation of Algebraic Expressions — all question types→Maths STD 8 question papers→Maharashtra Board STD 8 question papers→Maharashtra Board question paper generator→

Similar questions

Find the amount of Rs. 2400 after 3 years, when the interest is compounded annually at the rate of 20% per annum.
→
Find the product:
$4.1 x y(1.1 x-y)$
→
Simplify:
$\Big(\frac{3}{2}\times\frac{1}{6}\Big)+\Big(\frac{5}{3}\times\frac{7}{2}\Big)-\Big(\frac{13}{8}\times\frac{4}{3}\Big)$
→
Divide $a c x^2+(b c+a d) x+b d$ by $(a x+b)$
→
$1.8 \times 2.2$
→
Expand :

(m + 2n + 3r)²

→
Find the amount and the compound interest on Rs. 2500 for 2 years at 10% per annum, compounded annually.
→
By using the formula, find the amount and compound interest on.
Rs. 10240 for 3 years at $12\frac{1}{2}\%$ per annum compounded annually.
→
Which of the following are the cubes of even numbers?
  1. 216
  2. 729
  3. 512
  4. 3375
  5. 1000
→
Reena goes to a shop to buy a radio, costing Rs. 2,568. The rate of VAT is 7%. She tells the shopkeeper to reduce the price of the radio such that she has to pay Rs. 2,568 inclusive of VAT. Find the reduction needed in the price of radio.
→