Page 155 - ICSE Math 8

AT A GLANCE

¾ An algebraic identity is a statement of equality between two algebraic expressions that is satisfied by all
the values of the variables.
¾ Important identities:
(a) (a + b) = a + 2ab+ b 2 (b) (a – b) = a – 2ab + b 2 (c) (a + b)(a – b) = a – b 2
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¾ The trinomials a + 2ab + b and a – 2ab + b are known as perfect square trinomials.
¾ Special products:
(a) (x + a)(x + b) = x + (a + b)x + ab (b) (x + a)(x – b) = x + (a – b)x – ab
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(c) (x – a)(x + b) = x + (b – a)x – ab (d) (x – a)(x – b) = x – (a + b)x + ab
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MENTAL MATHS
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1. Find the value of a + b, when a – b = 1 and a – b = 7.
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2. Find the value of a – b, when a + b = 15 and a – b = 75.
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3. If a + b = 5 and ab = 6, find the value of a + b .
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4. If a – b = 3 and ab = 10, find the value of a + b .
PRACTICE TIME
1. Solve the following.
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(a) (2x + 3)(x + 4) (b)  3x + 1  2x + 4   (c) (x – 3)(y – 4) (d) (x – 7)(2x + 3)
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 y  y 
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(e) (x + 7)(x – 7) (f) (3 – x)(4 – x) (g) (3x + 4y)(3x – 4y)
2. Find the square of the following.
1 y
(a) 4a + 3b (b) 5x + (c) 3x – (d) 8x – 7y
2y 3
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3. If x + = 3, find the value of x + .
x x 2
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4. If x + = 34, find the value of x + .
x 2 x
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5. If x + y = 55 and xy = 3, find the value of x – y.
6. The length of a rectangular garden is given by (3x + 4) units. If the area is given by 6xy – 6x + 8y – 8,
find the breadth of the garden.
THINK SMART

1. A square field is divided into two identical rectangular fields of dimensions 5 m × 7 m, and two square
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fields of dimensions 7 m and 5 m each. Using the identity (a + b) , find the area of the bigger square field.
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2. What should added to 64x – 50xy + 9y to make it a perfect square trinomial?
3. Locate the errors and correct them in the following mathematical statements.
(i) 5(a + 4) = 5a + 4 (ii) p(2q + 3) = 2pq + p 3
(iii) 2a + 4b = 8ab (iv) 4x + 2x – x + x = 9x

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