Sheet13.9. Square of binomials:1Find the floor area of the house if it has four equal sides and one side measures x + 3.A= SA= (x + 3) = x + 2x(3) + 3 = x + 6x +92Find the area of a biggest circle that can be drawn inside the squareif half of its one side is 4x + 2.A= r = (4x + 2) = [16x + 2(4)(4x) + 4]= [16x + 32x + 4]= 4x + 8x + 43Solve the dimensions of the bed with each side is equally 1/2 meter awayfrom the walss if the area of the unoccupied space of bed is 36 meters.Let x = length of a side of the bed.x + 2 = the length of the roomArea of room less the unoccupied space = the area of the bed(x + 2) - x = 36; x + 2 (2) x + 4 -x = 364x + 4 = 36; 4x = 32; x= 32/4; x = 8 meters.3.10. Cube of a binomial1If a container with height is equal to its side is full of water, what is thevolume of water if one side is x + 2.V= (x + 2)= x + 3(x)(2) + 3 (x) (2) + (2)= x + 6 x + 12 x + 82How much volume of water needed to form an ice cube with dimensionof 4x + 3yV= (2x + 3y)= 8x + 3(4x)(3y)+ 3(2x)(9y) + 27y= 8x + 36xy+ 54xy + 27y3Solve the volume of a box which one side has a size of 5 + 3x.V = (5 +3x)= 125 + 3(25)(3x) + 3(5)(9x) + 27x= 125 + 225x + 135x + 27x3.11. Product of sums and differences1Get the volume of a rectangular box applying the concept of product of sums andand difference of the cube 2x +10 and 2x -10 and height of 4x.V = lwh= 4x (2x+10)(2x -10)4x= 4x (4x +20x -20x -100)= 4x (4x-100)2x + 10= 16 x-400x2x - 102Find the area of a retangle whose sides are binomials.If length is x + 3 and width is x -3.A = Lw= (x + 3)(x - 3)= x + 3 x - 3x -9= x-93What is the total area of land whose sides are 8x + 4 and 8x-4.A = LW= (8x + 4)(8x - 4)= 64x - 163.12. Squares of trinomials1Find the area of a square quilt having dimension of 6x + 3x + 4.(6x + 3x + 4);36x + 9x + 16 + 2(6x)(3x) + 2 (6x)(4) + 2(3x)(4);36x + 9x + 16 + 36x + 48x + 24x;36x + 36x + 57x + 24x + 16;2Solve the area of a square garden with one side measures 3x - 4y + 5z.(3x - 4y + 5z);9x + 16y + 25 z - 2(3x)(4y) + 2(3x)(5z) - 2(4y)(5z)9x + 16y + 25 z - 24xy + 30xz - 40yz3What is the area of a circle inscribed in a square whose side is 8a + 6b - 2c?A = r;= (8a + 6b - 2c)2= [64a + 36b +(- 2c)+ 2(8a)(6b) + 2(8a)(-2c) + 2(6b)(-2c)]= [64a + 36b + 4c+ 96ab - 32ac -24bc]= 64a + 36b + 4c+ 96ab - 32ac -24bc3.13 Division of Monomials.1Peter formed a rectangular prism out of a plain G.I. sheet. His teacher requiredhim to solve the number of cubes that can be filled shape inside the prism, if thevolume of the cube is 3x y.N= no. of cubesAV = (3x+ 2y)(3 y)(2x)= (3x)(6yx) + 2y(6yx)= (18xy) + (12yx)h=2xN = 18xy + 12yx3x yN = 6xy + 4y cubes3 yL=3x + 2y2In the figure B above, if h= 2x + 2, w= 10x, L=30x, compute the volume of water if itis halfly filled. If the water inside is frozen to ice, how many ice cube with volumex can be formed?V = (2x +2)(10x)(30x)= 600x + 600xC = no. of ice cubes= V/x= 600x + 600x2x=300 x + 300 xif x = 2C = 1200 + 600= 1800 ice cubes3How many tiles Mario will buy if the area of the floor is 38 xyz, and the tiledimension is 2x by yz.N = No. of tilesN = 38xyzA of the tile is Lw2xyzA = lw;N = 19xyz= 2x(yz)= 2xyz3.14 Division by polynomials to another polynomials1Find the length of a rectangle with an area of 3x + 7x + 11x + 3, and width of 3x + 1.A = LWL = A/Wx + 2x + 3= 3x + 7x + 11x + 33x + 13x + 7x + 11x + 33x + 13x + x= x + 2x + 36x + 11x6x + 2x9x + 39x + 302What is the height of the triangle having an area of 2x - 8x - 10x - 6 and whosebase is 2x + 2.A = bhh = 2A/b2x + 10x= 2(2x - 8x - 10x - 6)/2x + 2x - 12x + 8x - 10x -6= 2x -8x - 10x -62x - 2xx + 110x - 10x= 2x + 10x10x - 10x-63Solve for the quotient of this expression;4x - 6x + 12x - 42x + 4x - 42x - 12x - 14x + 6x - 12x -44x - 2xanswer= 2x + 4x - 48x - 12x8x - 4x- 8x -4- 8x +4-84.2Properties of Equality1A number diminished by 8 equals 25. What is the number?n= the numbern - 8 = 25n = 25 + 8n =332Twenty increased by a number equals 50. What is the number?n = the number20 + n = 50n = 50- 20n = 303Six times a number less ten equals 38. What is the number?n = the number6n -10 = 38n = 38 + 96n = 48/6n = 84.3Solving equations using addition or subtraction.1The birds are flying as high as the flagpole. What is the height of the flagpole if thebirds fly at a speed of 2 ft/sec and they reach the top of the pole at 5 seconds.h = height of the flagpoleh = 2ft/sec (5 sec)h = 10ft.2Fifty less than a number is thirteen.n - 50 = 13n = 13 + 50n = 633If Minda is taller than Kim, and kim is shorter than Melody by 2 inches, what is theheight of Minda if Melody is 62 inches tall and Kim stands 8 inches less than Minda.Given:Melody = 62 inchesKim = 62-2 = 60Let n = the height of Mindan -8 = 60n = 684.4.Solving equations using multiplications or divisions1The height of Eunice is 2 times greater than Mahal's height. What is the height ofof Eunice if Mahal is 1.5 ft tall?Let h = the height of Eunicen = the height of Mahalh = n + 2nh = 2.5 + 1.5 (2)h = 5.5 ft.2James bought a cloth for the unform of his basketball team players, if each pair ofuniform needs 2 meters, how many meters will James need to provide for the 1010 playersN = no. of meters James need for the playersN = 102N = 10 (2)N = 20 meters3Janine is asked to sell ballpens as part of fund raising of the student bodyorganization. She bought each box of the ball pen with 10 pcs in it by P50.00How many ball pens will she sell if she needs to raise Ph500 if she sells itat 9 pesos each.N = no. of ball pensN = 500/9- (50/10)= 500/ (9-5)= 500/4= 125 pcs4.5.Solving Multi-Steps Equation1A hotel charges a rate of Php1,500.00 per 8 hours of use of the function hall.In excess of 8 hours, the hotel management charges the amount of Ph300.00per hour of stay. If the hotel bills was P2,400.00, how many hours did the functionhall was in use?300 N + 1,500 = 2,400.00300 N + 1,500 = 2,400.00300300N + 5 = 8N + 5 - 5 = 8 - 5N = 32Twenty subtracted from the product of 4 and a number equals 28.N = a number4N -20 = 284N -20 + 20 = 28 + 204N = 484N = 484 4N = 123Eighteen less than four times a number equals 40.N = a number4N - 18 = 404N - 18 + 18 = 40 + 184N = 584N = 584 4N = 14.5

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