Question
Factorise : $(x^2+ 4y^2- 9z^2)^2- 16x^2y^2$
✓
Answer
$(x^2+ 4y^2- 9z^2)^2- 16x^2y^2= (x^2+ 4y^2- 9z^2)^2 - ( 4xy )^2$
$= ( x^2 + 4y^2 - 9z^2 - 4xy )( x^2 + 4y^2 - 9z^2 + 4xy ) [ \because a^2 - b^2 = ( a + b )( a - b )]$
$= ( x^2 + 4y^2 - 4xy - 9z^2 )( x^2 + 4y^2 + 4xy - 9z^2 )$
$= [( x - 2y )^2 - (3z)^2 ][ ( x + 2y )^2 - (3z)^2]$
$= [( x - 2y ) - 3z ][( x - 2y ) + 3z ][( x + 2y ) - 3z ][( x + 2y ) + 3z ]$
$= [ x - 2y - 3z ][ x - 2y + 3z ][ x + 2y - 3z ][ x + 2y + 3z ]$
$= ( x^2 + 4y^2 - 9z^2 - 4xy )( x^2 + 4y^2 - 9z^2 + 4xy ) [ \because a^2 - b^2 = ( a + b )( a - b )]$
$= ( x^2 + 4y^2 - 4xy - 9z^2 )( x^2 + 4y^2 + 4xy - 9z^2 )$
$= [( x - 2y )^2 - (3z)^2 ][ ( x + 2y )^2 - (3z)^2]$
$= [( x - 2y ) - 3z ][( x - 2y ) + 3z ][( x + 2y ) - 3z ][( x + 2y ) + 3z ]$
$= [ x - 2y - 3z ][ x - 2y + 3z ][ x + 2y - 3z ][ x + 2y + 3z ]$
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
Find $x,$ if $:\log_432 = x - 4$
→In the given figure, $AB = AC$. If BO and CO , the bisectors of $\angle B$ and $\angle C$ respectively meet at O and BC is produced to D , prove that $\angle BOC =\angle ACD$.
→If $\left(x-\frac{1}{x}\right)=4$, find the values of (i) $\left(x^2+\frac{1}{x^2}\right)$ (ii) $\left(x^4+\frac{1}{x^4}\right)$.
→Express in terms of $\log 2$ and $\log 3 :\log \frac{26}{51}-\log \frac{91}{119}$
→The following table shows the weights (in kg) of 15 workers in a factory :
Calculate the mean weight.
| Weight (in kg) | 60 | 63 | 66 | 72 | 75 |
| Number of workers | 4 | 5 | 3 | 1 | 2 |
The value of a machine depreciates 10% annually. Its present value is ₹64800. Find:
(i) its value after 2 years,
(ii) its value 2 years ago.
(i) its value after 2 years,
(ii) its value 2 years ago.
If $2250=2^a \cdot 3^b \cdot 5^c$, find $a, b$ and $c$. Hence, calculate the value of $3^a \times 2^{-b} \times 5^{-c}$.
→Evaluate the without using log table:
$2 \log 5+\log 8-\frac{1}{2} \log 4$
→$2 \log 5+\log 8-\frac{1}{2} \log 4$
The cross-section of a tunnel, perpendicular to its length is a trapezium ABCD in which AB = 8m DC 6 m and AL = BM The height of the tunnel is 2.4 m and its length is 40 m.
Find:
(i) the cost of paving the floor of the tunnel at 16 per m ^ 2
(ii) the cost of painting the internal surface of the tunnel, excluding the floor at the rate of 5 per $m ^2$
→Find:
(i) the cost of paving the floor of the tunnel at 16 per m ^ 2
(ii) the cost of painting the internal surface of the tunnel, excluding the floor at the rate of 5 per $m ^2$
If $A = B = 60^\circ ,$ verify that$: \sin(A - B) = \sin A \cos B - \cos A \sin B$
→