Please help me with this

6,561

39,204

25,575

52.5625 - 7.5625 = 45

Step-by-step explanation:

(i)

(81)^2

Use (a + b)^2 = a^2 + 2ab + b^2

(81)^2 = (80 + 1)^2 =

= 80^2 + 2 * 80 * 1 + 1^2

= 6400 + 160 + 1

= 6561

(ii)

(198)^2

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

(198)^2 = (200 - 2)^2 =

= 200^2 - 2 * 200 * 2 + 2^2

= 40,000 - 800 + 4

= 39,204

(iii)

165 * 155

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

165 * 155 = (160 + 5)(160 - 5) =

= 160^2 - 5^2

= 25,600 - 25

= 25,575

(iv)

(7.25)^2 - (2.75)^2

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

(7.25)^2 - (2.75)^2 =

= (7.25 + 2.75)(7.25 - 2.75)

= 10(4.5)

= 45

the quotient is 4x^2 - 27x + 167 with a remainder of -996

step-by-step explanation:

in synthetic division, use -6 as the divisor and use the coefficients {4, -3, 5, 6}:

-6     )   4     -3     5     6

                -24   162 -1002

          4   -27   167   -996

thus, the quotient is 4x^2 - 27x + 167 with a remainder of -996.

note:   your "4x°-3x+5x+6" is ambiguous / incomplete.   i had to assume that you meant '4x^3 - 3x^2 + 5x + 6."

use this formula:

p(a\b) = p(a and b)/p(b).

take it from here.