Verified answer

Step-by-step explanation:

9(a):-

18ab(16a^2-9b^2)÷(9ab(4a+3b)

=>(2×9ab)[(4a)^2-(3b)^2]÷(9ab(4a+3b))

=>(2×9ab)(4a+3b)(4a-3b)÷(9ab(4a+3b))

=>9ab(4a+3b)[2+4a-3b]÷(9ab(4a+3b))

=>9ab(4a+3b)[2+4a-3b]/(9ab(4a+3b))

=>4a-3b+2

18ab(16a^2-9b^2)÷(9ab(4a+3b) = 4a-3b+2

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9(b):-

(p^2-5p+6)÷(p-2)

=>(p^2-2p-3p+6)/(p-2)

=>[p(p-2)-3(p-2)]/(p-2)

=>(p-2)(p-3)/(p-2)

=>p-3)

(p^2-5p+6)÷(p-2) = (p-3)

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10(a):-

7a^2b^2+b^2 simplifies to 7a^2b^2 is wrong

addition is wrong

=>7a^2b^2+b^2

=>b^2(7a^2+1)

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10(b):-

7x/(7x+8) is simplifies to 1/8

Division is wrong

7x/(7x+8)

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10(c):-

(4p-7q)(4p+7q) simplifies to 16p^2+49q^2 is wrong

(4p-7q)(4p+7q)

this is in the form of (a+b)(a-b).

Where, a= 4p

b=7q

we know that

(a+b)(a-b) = a^2-b^2

(4p-7q)(4p+7q)

=>(4p)^2-(7q)^2

=>16p^2-49q^2

(4p-7q)(4p+7q) = 16p^2-49q^2

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10(d):-

65x^3/65x^3 simplifies to 0

This Division is wrong

=>65x^3/65x^3

=>1

65x^3/65x^3 = 1

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11.

Given equation is x^2+ax-2 = (x-1)(x+b)

=>x^2+ax-2 = x^2+bx-x-b

=>x^2+ax-2 = x^2+(b-1)x-b

On comparing both sides then

b=2 and

=>a=b-1

=>a=2-1

=>a =1

The value of a = 1 and b=2

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12.

Given pilynomial is a^2-24a+114

We know that by factor theorem

If P(x) is a polynomial and (x-a) is a factor then P(a)=0

Now a-12 = 0=>a=12

Now P(a)=a^2-24a+114

=>P(12)=(12)^2-24(12)+114

=>144-288+114

=>258-288

=>-30

So, (a-12) is not a factor of a^2-24a+114

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13.

Given that

Area of a square = (4a^2+6a+6a+9) sq.units

Area of a square = side×side

=>Side×Side = 4a^2+6a+6a+9

=> Side×Side= 2a(2a+3)+3(2a+3)

=>Side ×Side = (2a+3)(2a+3)

Length of the side of the square = (2a+3) units

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