# algebra coursework

Algebra Coursework

Ex 1

2 X 2 square on 10 X 10 grid

12 X 23 = 276
13 X 22 = 286

286 – 276 = 10

Z = Top left number = 12 (in this case)
Z+1 = 12 +1 = 13 (top right number)
Z+10 = 12+10 = 22 ( bottom left number)
Z+11= 12+11 = 23 ( bottom right  number)

Z (Z+11) = Z² + 11Z

(Z+1) (Z+10) = Z² +10Z + Z +10
= Z² + 11Z + 10

Z² + 11Z + 10 – Z² + 11Z = 10

Ex 2

2 X 2 square on 10 X 10 grid

74 X 85 = 6290
84 X 75 = 6300

6300 – 6290 = 10

Z = Top left number = 74 (in this case)
Z+1 = 74+1 = 75 ( top right number )
Z+10 = 74+10 = 84 ( bottom left number)
Z+11= 74+11 = 85 ( bottom right number)

Z (Z+11) = Z² + 11Z

(Z+1) (Z+10) = Z² +10Z + Z +10
= Z² + 11Z + 10

Z² + 11Z + 10 – Z² + 11Z = 10

Ex 3

3 X 3 square on 10 X 10 grid

48 X 70 = 3360
68 X 50 = 3400

3400 – 3360 = 40

Z = top left number = 48 (in this case)

Z+2 = 48 +2 = 50 (top right number)

Z+20 = 48 +20 = 68 (bottom left number)

Z+22= 48 +22 = 70 (bottom right number)

Z (Z+22) = Z² + 22Z

(Z+2) (Z+20) = Z² + 20Z +2Z +40

= Z² + 22Z + 40

Z² + 22Z + 40 - Z² + 22Z = 40

Ex 4

4 X 4 square on 10 X 10 grid

7 X 40 = 280

10 X 37 = 370

370 – 280 = 90

Z = top left number = 7 (in this case)

Z+3 = 7 + 3 = 10 (top right number)

Z+30 = 7 + 30 = 37 (bottom left number)

Z+33 = 7+33 = 40 (bottom right number)

Z (Z+33) = Z² + 33 Z

(Z+3) (Z+30) = Z² + 30Z + 3Z + 90

= Z² + 33Z + 90

Z² + 33Z + 90 - Z² + 33Z = 90

Ex 5

5 X 5 square on 10 X 10 grid

32 X 76 = 2432

36 X 72 = 2592

2592 – 2432 = 160

Z = top left number = 32 (in this case)

Z+4 = 32 + 4 = 36 (top right number)

Z+40 = 32 + 40 = 72 (bottom left number)

Z+44 = 32 + 44 = 76 (bottom right number)

Z (Z+44) = Z² + 44Z

(Z+4) (Z+40) = Z² + 4Z + 40Z + 160

= Z² + 44Z + 160

Z² + 44Z + 160 - Z² + 44Z = 160

Table

The Square formula for a 10X10 grid

X times X square

X

X

2 X 2 square

Z = top left ...