Question
Factorise the following using the identity $a^2- b^2= (a + b)(a - b).$
$\text{x}^2-\frac{\text{y}^2}{100}$
$\text{x}^2-\frac{\text{y}^2}{100}$
✓
Answer
$\text{x}^2-\frac{\text{y}^2}{100}$$=\text{x}^2-\Big(\frac{\text{y}}{10}\Big)^2$
$=\Big(\text{x}+\frac{\text{y}}{10}\Big)\Big(\text{x}-\frac{\text{y}}{10}\Big)$
$=\Big(\text{x}+\frac{\text{y}}{10}\Big)\Big(\text{x}-\frac{\text{y}}{10}\Big)$
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Algebraic Tiles
(i) Cut the following tiles from a graph sheet. Now, colour the tiles as per the colour code. Arrange these algebraic tiles to form a square.
Find the length of the side of the square so formed. Also find the area of the square. Using the above result factorise $x^2+4 x+4$.
(ii)
Find the length of the side of the rectangle so formed. Also, find the area of the rectangle. Using the above result factorise $x^2+5 x+4$.
Now, choose and cut more algebraic tiles from the graph sheet. Create your own colour code and colour the tiles. Arrange them to form square/rectangle. Find the area of the figure so formed using it to factorise
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→(i) Cut the following tiles from a graph sheet. Now, colour the tiles as per the colour code. Arrange these algebraic tiles to form a square.
Find the length of the side of the square so formed. Also find the area of the square. Using the above result factorise $x^2+4 x+4$.
(ii)
Find the length of the side of the rectangle so formed. Also, find the area of the rectangle. Using the above result factorise $x^2+5 x+4$.
Now, choose and cut more algebraic tiles from the graph sheet. Create your own colour code and colour the tiles. Arrange them to form square/rectangle. Find the area of the figure so formed using it to factorise
(a) $x^2+4 x+3$ $\qquad$ (b) $x^2+9 x+18$
(iii) Build a square garden. Divide the square garden into four rectangular flower beds in such a way that each flower bed is as long as one side of the square. The perimeter of each flower bed is 40 m .
(a) Draw a diagram to represent the above information.
(b) Mention the expression for perimeter of the entire garden.
Factorise:
$p^2+6 p+8$
→$p^2+6 p+8$
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Find the mid-point of $\overline{A C}$ by a fold, placing $C$ on $A$. Is the mid-point same as O?
Does this show that diagonal $\overline{D B}$ bisects the diagonal $\overline{A C}$ at the point $O$ ? Discuss it with your friends.
Repeat the activity to find, where the mid-point of $\overline{D B}$ could lie.
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Does this show that diagonal $\overline{D B}$ bisects the diagonal $\overline{A C}$ at the point $O$ ? Discuss it with your friends.
Repeat the activity to find, where the mid-point of $\overline{D B}$ could lie.
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