Question
Factorise:
$125 - 8x^3 - 27y^3 - 90xy$
$125 - 8x^3 - 27y^3 - 90xy$
✓
Answer
$125 - 8x^3 - 27y^3 - 90xy$
$= 5^3 + (-2x)^3 + (-3y)^3 - 3 \times 5 \times (-2x) \times (-3y)$
$= [5 + (-2x) + (-3y)][5^2 + (-2x)^2 + (-3y)^2 - 5 \times (-2x) - (-2x)(-3y) - 5 \times (-3y)]$
$= (5 - 2x - 3y)(25 + 4x^2 + 9y^2 + 10x - 6xy + 15y)$
$= 5^3 + (-2x)^3 + (-3y)^3 - 3 \times 5 \times (-2x) \times (-3y)$
$= [5 + (-2x) + (-3y)][5^2 + (-2x)^2 + (-3y)^2 - 5 \times (-2x) - (-2x)(-3y) - 5 \times (-3y)]$
$= (5 - 2x - 3y)(25 + 4x^2 + 9y^2 + 10x - 6xy + 15y)$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Verify that:
1 and 2 are the zeros of the polynomial $p(x)=x^2-3 x+2$.
→1 and 2 are the zeros of the polynomial $p(x)=x^2-3 x+2$.
Compare the following : $\quad \frac{9.2}{5.1}, \frac{3.4}{7.1}$
→Define the following terms:
Line segment.
Line segment.
In how many points two distinct planes can intersect?
Express the following equation in the form ax + by + c = 0 and indicate the values of a, b, c in case.
4y = 7
4y = 7
In the adjoining figure, ∠ACD is an exterior angle of ∆ABC. ∠B = 40°, ∠A = 70°. Find the measure of ∠ACD.
Factorise:$2\text{x}^2+3\sqrt{3}\text{x}+3$
→Find the following products:
$(3 x+2 y)\left(9 x^2-6 x y+4 y^2\right)$
→$(3 x+2 y)\left(9 x^2-6 x y+4 y^2\right)$
hemispherical bowl is made of steel 0.25cm thick. The inside radius of the bowl is 5cm. Find the volume of steel used in making the bowl.
The inner diameter of a well is 4.20 metre and its depth is 10 metre. Find the inner surface area of the well. Find the cost of plastering it from inside at the rate ₹ 52 per sq.m.
Given: Inner diameter (d) = 4.2 m,
To find: depth (h) = 10 m,
rate of plastering = ₹ 52 per sq.m.
Inner surface area and total cost of plastering
Given: Inner diameter (d) = 4.2 m,
To find: depth (h) = 10 m,
rate of plastering = ₹ 52 per sq.m.
Inner surface area and total cost of plastering