Find a polynomial that represents the perimeter of the figur

Find a polynomial that represents the perimeter of the figure below. Multiply the polynomials. -x^2y(6xy - 23/3 x^2 + 19/2 y^4) Multiply the polynomials. (11t - s) (t + 5s) Multiply the polynomials. (10z + 5) (z^2 - 2z + 2) Multiply the conjugates. (8x - 9) (8x + 9) Multiply the conjugates. (-8z + 3t) (-8z - 3t) Square the binomial. (2w - 4t)^2 If the length of one side of a square is given by 5x^2 - 8x, find and simplify a polynomial that describes the area of the square. Find a polynomial that represents the area of the figure below.

Solution

30. The polynomial is p(a) =a² + a+2a² +a -5+2a² -18 = 5a²+2a -23.

31. –x²y[ 6xy -23x²/3+19y⁴/2] = -6x³y²+ 23x⁴y/3 - 19x²y⁵/2 = 23x⁴y/3-6x³y²- 19x²y⁵/2.

32. (11t-s)(t+5s) = 11t² –st +55st -5s² = -5s²+54st +11t²

33.(10z+5)(z²-2z+2) = 10z³ +5z²-20z²-10z +20z +10 = 10z³ -15z²+10z +10

34.(8x-9)(8x+9) = (8x)²-9² = 64x² -81 [ as (a-b)(a+b) = a² –b² ]

35.(-8z+3t)(-8z-3t) = (-8z)² –(3t)² = 64z²-9t²

36.(2w-4t)² = (2w)² -2*2w*4t +(4t)² = 4w²-16wt+ 16t² [ as (a-b)² = a² -2ab+b² ]

37. The side of a square is 5x²-8x. Then its area is side²=(5x²-8x )²=(5x²)²-2*5x²*8x+(8x)²= 25x⁴-80x³+64x²

38. There is no figure.