Solve: 1 16 x^2y^2-4 49 y^2z^2 - Vidyadip

Question

Solve: $\frac{1}{16}\ \text{x}^2\text{y}^2-\frac{4}{49}\text{y}^2\text{z}^2$

✓

Answer

$\frac{1}{16}\ \text{x}^2\text{y}^2-\frac{4}{49}\text{y}^2\text{z}^2$
$=\text{x}^2\text{y}^2\Big(\frac{1}{16}\ \text{x}^2-\frac{4}{49}\ \text{z}^2\Big)$
$=\text{y}^2\Big[\Big(\frac{1}{4}\ \text{x}\Big)^2-\Big(\frac{2}{7}\ \text{z}\Big)^2\Big]$
$=\text{y}^2\Big(\frac{1}{4}\ \text{x}\ -\frac{2}{7}\ \text{z}\Big)\Big(\frac{1}{4}\ \text{x}+\frac{2}{7}\text{z}\Big){}$
$=\text{y}^2\ \Big(\frac{\text{x}}{4}-\frac{2}{7}\ \text{z}\Big)\Big(\frac{\text{x}}{4}+\frac{2}{7}\ \text{z}\Big)$

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 Marks Question" from Factorization→Factorization — all question types→MATHS STD 8 question papers→Gujarat Board STD 8 question papers→Gujarat Board question paper generator→

Similar questions

Subtract: $\frac{3}{2}\text{x}-\frac{5}{4}\text{y}-\frac{7}{2}\text{z}$ from $\frac{2}{3}\text{x}+\frac{3}{2}\text{y}-\frac{4}{3}\text{z}$

If $x$ and $y$ vary inversely and $x = 18$ when $y = 8$, find $x$ when $y = 16.$

Find the square root of the following correct to three places of decimal:$0.016$

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.

A square sheet of paper is converted into a cylinder by rolling it along its side. What is the ratio of the base radius to the side of the square?

A dealer purchased a fan for $Rs. 1080.$ After allowing a discount of $25\%$ on its marked price, he gains $25\%.$ Find the marked price of the fan.

Write a Pythagorean triplet whose one number is $18$

Find the cube root of each of the following natural numbers:
$4913$

If $\frac{3}{5}$ of a number exceeds its $\frac{2}{7}$ by $44,$ find the number.

Factorise the expressions: $p^2 6p – 16$