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Let’s say and write the differences of these squared numbers as quickly as possible.
a) $10^2 – 9^2 =$ ………………..
b) $7^2 – 5^2 =$ ………………..
c) $21^2 – 20^2 =$ ………………..
d) $50^2 – 49^2 =$ ………………..
e) $20^2 – 10^2 =$ ………………..
f) $40^2 – 30^2 =$ ………………..
Let’s resolve into factors.
a) $x^2 – 36$
b) $a^2 – 49$
c) $25 – y^2$
d) $16 – 81p^2$
e) $x^3 – 16x$
f) $2a^2 – 72$
g) $5p^3 – 80p$
h) $3y^3 – 27y$
i) $5a^3 – 20ab^2$
j) $8x^5y – 18x^3y^3$
k) $25x^2 – frac{1}{49}$
l) $frac{1}{4x^2} – frac{1}{81}$
Let’s say and write the following expressions as the product of their factors.
| Expressions | Product of factors | Expressions | Product of factors |
| a) $m^2 – n^2$ | f) $4x^2 – 1$ | ||
| b) $m^2 – 4$ | g) $9y^2 – 4$ | ||
| c) $x^2 – y^2$ | h) $p^2 – 49$ | ||
| d) $x^2 – 9$ | i) $a^2 – frac{1}{4}$ | ||
| e) $p^2 – 16$ | j) $b^2 – frac{1}{9}$ |
a) If $(4ax + 6ay)$ sq. unit is the area of a rectangle, find the length and breadth of the rectangle.
b) Find the length and breadth of a rectangle of area $(2x^2 + 2xy + xy + y^2)$ sq. unit. Also, find the perimeter of the rectangle.
c) The area of a rectangular field is $(x^2 + 3xy + 2xy + 6y^2)$ sq. unit. Find the perimeter of the field.
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Let’s find the length and breadth of the following rectangles of the given area.
a) Area $= 3a^2b + 6ab$
b) Area $= x^2 + 2x + xy + 2y$
c) Area $= x^2 + 3x + 4ax + 12a$
Let’s resolve into factors.
a) $ax + ay + bx + by$
b) $px + qx – py – qy$
c) $x^2 + 2x + 3x + 6$
d) $x^2 – 4x – 3x + 12$
e) $6x^2 – 2y^2 + 4xy – 3xy$
f) $ax^2 + ay^2 + bx^2 + by^2$
g) $x^3 + x^2 + x + x^2y + xy + y$
h) $x^2 – x(y + z) + yz$
i) $a^2 – a(2x – y) – 2xy$
j) $x^2 – (y – 3)x – 3y$
k) $x(a^2 – b^2) + a(b^2 – x^2)$
l) $ab(c^2 + 1) – c(a^2 + b^2)$
Let’s factorise
a) $2ax + 4ay$
b) $6x^2 – 9x$
c) $8px^3 + 12px^2$
d) $4mx^2 – 6mx + 2m^2x$
e) $9b^2y^3 – 6b^3y^2 + 15b^2y^2$
f) $-9a^5 – 6a^3x^2 – 15a^2$
g) $x(2x + 3) + 4(2x + 3)$
h) $2y(y – 4) – 3(y – 4)$
i) $7x(x + 2y) + y(x + 2y)$
Let’s apply the process of factorisation and simplify.
a) $15 times 6 + 15 times 4$
b) $3.4 times 10^3 – 2.6 times 10^3$
c) $3.5 times 10^{-2} + 2.3 times 10^{-2}$
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Factorize :
a) $x(a + b) + y(a + b) =$ ………………..
b) $a(p + q) – (p + q) =$ ………………..
c) $(y – 2) – y(y – 2) =$ ………………..
d) $x(a – b) + 2(a – b) =$ ………………..
a) If $a + frac{1}{a} = 3$, find the values of (i) $a^2 + frac{1}{a^2}$ (ii) $left(a – frac{1}{a}right)^2$
b) If $x + frac{1}{x} = 5$, find the values of (i) $x^2 + frac{1}{x^2}$ (ii) $left(x – frac{1}{x}right)^2$
c) If $p – frac{1}{p} = 4$, find the values of (i) $p^2 + frac{1}{p^2}$ (ii) $left(p + frac{1}{p}right)^2$
