Question

any maths expert here please help me out please answer anyone of these
please give step by step explanation along with the answer please no spamming​

Answer 1

Step-by-step explanation:

(6) (103)³ can be written as (100+3)³

=100³+3³+3x100²x3+3x100+3²

=1000000+27+90000+2700

=1902727

(7) 2a-1=0

=> a= ½

Then it is easy just substitute ½ everywhere where it is a

=> 6(½)²-7(½)-5

=6/4-7/2-5

=3/2-7/2-5

=-4/2-5

=-2-5

= -7

(8) Area=x²+9x+8

Factorise by splitting the middle term,

x²+8x+x+8

=x(x+8)+1(x+8)

=(x+1)(x+8)

You can take anyone of them as the length and breadth is given as x+6

Hope you like my answer

Answer 2

6. Evaluate using suitable Identity: (103)²

Sol: We can write (103)³ as (100+3)³

Now, Using identity: (a+b)³ = a³ + b³ + 3ab(a+b)

(103)³ = (100 + 3)³

= (100)³ + (3)³ + 3(100)(3)(100 + 3)

= 1000000 + 27 + 900(103)

= 1000027 + 92700

= 1092727

$\rule{200}2$

7. Find the quotient and remainder when (6a² - 7a - 5) is divided by (2a - 1).

Sol:

2a-1 ) 6a² - 7a - 5 ( 3a - 2

..........6a² - 3a [change the signs]

_________________

............... - 4a - 5

............... - 4a + 2 [change the signs]

______________________

...................... - 7

Quotient is 3a - 2 and Remainder is -7.

$\rule{200}2$

8. The area of rectangle is x² + 9x + 18. If breadth is (x + 6), find it's length.

Sol. Let us assume that Length is M.

Area of rectangle = Length × Breadth

x² + 9x + 18 = M × (x + 6)

x² + 3x + 6x + 18 = M × (x + 6)

x(x + 3) + 6(x + 3) = M × (x + 6)

(x + 6)(x + 3) = M(x + 6)

(x + 3) = M

Length = (x + 3)