Question

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Answer 1

Answer:

1. Simplify

a) $-4xy(-3x^{2} y + 4x)$ $=12x^{3} y^{2} - 16x^{2}y$

b) $(8y - 5x)(8y + 2x) = 64y^{2} - 24xy - 10x^{2}$

c) $(\frac{3}{2} x - 3y )(-4x + 2y) = -6x^{2} + 15xy -6y^{2}$

d) (9xy - 4yz) + (3yx - 2zy) = 12xy - 6yz

e) $(12xy + 8) - (15x^2 - 30x) = - 15x^2 + 12xy + 30x + 8$

f) $a = 2\sqrt{10}$

2.  Find the values using identities

(i) $(12a - 13b)^2 = 144a^2 - 312ab + 169b^2$

(ii) $(5y + 9z)^2 = 25y^2 + 90yz + 81z^2$

(iii) $(6a - 13b)(6a + 13b) = 36a^2 - 169b^2$

(iv) $(2a + 3)(2a - 5) = 4a^2 - 4a - 15$

(v) $99^2 = 9801$

(vi) $65^2 = 4225$

(vii) $197 . 203 = 39,991$

(viii) $67^2 - 57^2 = 1240$

3. Simplify

(a) $3a^2(a^3 - b^3) - 3b^2(a^2 - b^2) = 3a^5 - 3a^2b^3 - 3a^2b^2 + 3b^4$

(b) $7a(2a - 5) - 8a(3a^2) - 5a(2a + 5)$ $= - 24a^3 + 4a^2 - 60a$

(c) $(x^2 + 2)(x^2 - 7) = x^4 - 7x^2 + 2x^2 - 14 = x^4 - 5x^2 - 14$

(d) $z = 952$

Step-by-step explanation:

1. Simplify

a) $-4xy(-3x^{2} y + 4x)$ $=12x^{3} y^{2} - 16x^{2}y$

b) (8y - 5x)(8y + 2x) $= 64y^{2} + 16xy - 40xy - 10x^{2} = 64y^{2} - 24xy - 10x^{2}$

c) $(\frac{3}{2} x - 3y )(-4x + 2y) = -6x^{2} + 3xy + 12xy -6y^{2} = -6x^{2} + 15xy -6y^{2}$

d) (9xy - 4yz) + (3yx - 2zy) = 12xy - 6yz

e) $(12xy + 8) - (15x^2 - 30x) = - 15x^2 + 12xy + 30x + 8$

f) $6a^{2} = 23^2 - 17^2 = (23 + 17)(23 - 17) = 40.6$

∴ $a^{2} = 40$,  ∴ $a = \sqrt{40} = 2\sqrt{10}$

2.  Find the values using identities

(i) $(12a - 13b)^2 = (12a)^2 - 2.12a.13b + (13b)^2 = 144a^2 - 312ab + 169b^2$

(ii) $(5y + 9z)^2 = 25y^2 + 2.5y.9z + 81z^2 = 25y^2 + 90yz + 81z^2$

(iii) $(6a - 13b)(6a + 13b) = 36a^2 - 169b^2$

(iv) $(2a + 3)(2a - 5) = (2a + 3)(2a - 3 -2) = (2a + 3)(2a - 3) -2(2a + 3) = 4a^2 - 9 - 4a - 6 = 4a^2 - 4a - 15$

(v) $99^2 = (100 - 1)^2 = 100^2 - 2.100.1 + 1^2 = 10000 - 200 + 1 = 9801$

(vi) $65^2 = (60 + 5)^2 = 60^2 + 2.60.5 + 5^2 = 3600 + 600 + 25 = 4225$

(vii) $197 . 203 = (200 - 3)(200 + 3) = 200^2 - 3^2 = 40000 - 9 = 39,991$

(viii) $67^2 - 57^2 = (67 + 57)(67 - 57) = 124 . 10 = 1240$

3. Simplify

(a) $3a^2(a^3 - b^3) - 3b^2(a^2 - b^2) = 3a^5 - 3a^2b^3 - 3a^2b^2 + 3b^4$

(b) $7a(2a - 5) - 8a(3a^2) - 5a(2a + 5) = 14a^2 - 35a - 24a^3 - 10a^2 - 25a$

$= - 24a^3 + 4a^2 - 60a$

(c) $(x^2 + 2)(x^2 - 7) = x^4 - 7x^2 + 2x^2 - 14 = x^4 - 5x^2 - 14$

(d) $6z = 76^2 - 8^2 = (76 + 8)(76 - 8) = 84 . 68$

∴ $z = \frac{84 . 68}{6} = 14 . 68 = 952$

Answer 2

Answer:

Perfect questions for guys interested in maths..

2. The value of x + x(xx) when x = 2 is:

(a) 10, (b) 16, (c) 18, (d) 36, (e) 64

Solution:

x + x(xx)

Put the value of x = 2 in the above expression we get,

2 + 2(22)

= 2 + 2(2 × 2)

= 2 + 2(4)

= 2 + 8

= 10

Answer: (a)