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Algebra. Collecting Terms. This is a way of simplifying algebra If you have b + b + b + b This is the same as 4 b The b could stand for boots If you have p x p x p This is p 3 This happens when multiplying. Try these:. M x m T + t + t R x r x r x r G + g + g + g H x h x h

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collecting terms
Collecting Terms
  • This is a way of simplifying algebra
  • If you have b + b + b + b
  • This is the same as 4 b
  • The b could stand for boots
  • If you have p x p x p
  • This is p3
  • This happens when multiplying
try these
Try these:
  • M x m
  • T + t + t
  • R x r x r x r
  • G + g + g + g
  • H x h x h
  • K + k
  • J x j x j x j x j x j x j
answers
Answers
  • M2
  • 3t
  • R4
  • 4g
  • H3
  • 2k
  • j7
collecting terms1
Collecting terms
  • Usually you have to collect terms from a mix
  • You cannot add 2t and t2, you can only add t2 and t2 together
  • E.g.
  • A2 + 3a + 3a + 2a2
  • 3a + 3a = 6a
  • A2 + 2a2 = 3 a2
  • So the simplified equation is 6a + 3 a2
collecting terms2
Collecting terms
  • You may have to deal with minus numbers or terms
  • Always look at the sign before the term to see if it is positive (+) or negative (-)
  • E.g. 3 -1 -4
  • This is +3 and -1 and -4
  • 3 -1 = 2
  • 2 - 4 = -2
now try these
Now try these;
  • -5 +4 -3
  • 3h + 2h – 6h
  • 3s + 3s – 8s
  • 7y – 5y – 2y
  • 3d – d + 2d – 5d
  • 7r – 4r – 5r -2r
  • 5p – p + 3p – 2p
answers1
Answers
  • -4
  • -1h or -h
  • -2s
  • 0
  • -1d or –d
  • -4r
  • 5p
mixed terms
Mixed terms
  • J + j + k + k + k
  • R – 2r +3s +2s
  • 7y – 5y – 3y +4
  • 3t + 6s – 8s + t
  • 7r + 2s – r – s
  • 5p + 6 – 7p – 9
  • 3a + b + a - 2b
answers2
Answers
  • 2j + 3k
  • -r + 5s
  • -y + 4
  • 4t – 2s
  • 6r + s
  • -2p – 3
  • 4a - b
multiplying terms
Multiplying Terms
  • When you multiply terms you multiply the numbers at the start of the term and then add together the number of letters you have
  • E.g.
  • 2a x 3a
  • This is 2 x 3 = 6
  • And a x a = a2
  • This is 6a2
multiplying
Multiplying
  • 2 x 4c
  • 2 x r x s
  • 5 x 3c
  • 2e x 6e
  • 3a x 2a
  • (4k)2
  • 4r x 2rs
answers3
Answers
  • 8c
  • 2rs
  • 15c
  • 12e2
  • 6a2
  • 16k2
  • 8r2s
try these1
Try these
  • 5ab – 3ab
  • 6vw – 4w + 5wv
  • X + 2x – 3x2 + 5x2
  • 8r + 6rs – 2sr – 3r
  • Xy + x2 – 3xy + 3x2
  • 4y + 3y2 – 7y2 – 2y
answers4
Answers
  • 2ab
  • 11 vw + 4w
  • 3x + 2x2
  • 5r – 4rs
  • -2xy + 4x2
  • 2y – 4y2
multiplying out brackets
Multiplying Out Brackets
  • Everything inside the brackets is multiplied by the term just outside it to the left
  • E.g.
  • 4 (3 + t)
  • This is
  • 4 x 3 = 12
  • And 4 x t= 4t
  • So it becomes 12 + 4t
try these2
Try these
  • 6(1-s)
  • 4(p + q)
  • 3(10j-4k)
  • R2(3-2s)
  • 2x3 (x-y)
  • 5t2 (s + t)
  • 3r (2r – 3s – t)
answers5
Answers
  • 6 -6s
  • 4p + 4q
  • 30j + 12k
  • 3r2 + -2r2s
  • 2x4 – 2x3y
  • 5st2 + 5t3
  • 6r2 – 9rs – 3rt
factorising
Factorising
  • This is the opposite of multiplying out brackets
  • When you simplify you can place terms inside brackets
  • E.g. 4k + 2
  • Both can be divided by 2
  • So it becomes 2(2k + 1)
  • Everything inside the bracket is divided by 2
try these3
Try these
  • 3f + 3
  • 15 + 20 t
  • 18 + 6a
  • 10j + 25
  • 3r + 3s + 3t
  • Pq – q2
  • 24p2 + 30pq
  • 20ab2 + 36a2b2
answers6
Answers
  • 3 (f + 1)
  • 5 (3 + 4t)
  • 6 (3 + a)
  • 5 (2j + 5)
  • 3 (r + s + t)
  • Q (p – q)
  • 6p (4p + 5q)
  • 4ab (5b + 9ab)
multiplying brackets with
Multiplying Brackets with -
  • If there is a minus before the brackets
  • A minus x a plus = a minus
  • A minus x a minus = a plus
  • E.g.
  • -3(2r – r)
  • -3 x 2r= -6r
  • -3 x –r = +3r
  • So it becomes -6r + 3r
try these4
Try these
  • -8(s-t)
  • -(r-5)
  • -(4r-3)
  • -9y(y-1)
  • -5s(s+4)
  • -3h(5-h)
  • - (x+y)
answers7
Answers
  • -8s + 8t
  • -r + 5
  • -4r + 3
  • -9y2 + 9y
  • -5s2 + 20s
  • -15h + 3h2
  • -x - y
multiplying sets of brackets
Multiplying sets of brackets
  • If you are given 2(3+y) + 5(4+y)
  • First you must multiply out the brackets
  • 6 + 2y + 20 + 5y
  • Secondly you collect terms
  • 26 + 7y
try these5
Try these
  • 3(4+d)+4(2+d)
  • 6(3+x)+5(2-x)
  • 2(10+5e)-3(6+e)
  • 3(4r+1)-(7r-2)
  • 4(w+1)-(w-1)
  • X(2x+1)+2(3x+4)
  • 4(5+2f)+f(3+f)
answers8
Answers
  • 20 + 7d
  • 28 + x
  • 2 + 7e
  • 5r + 5
  • 3w + 5
  • 2x2 + 7x + 8
  • 20 + 11f + f2
multiplying out brackets1
Multiplying out brackets
  • If you are given (y+2)(y-4)
  • Then you really have two sums
  • Y(y-4)
  • +2 (y-4)
  • We have split the first bracket up to make sure we multiply everything together
  • So what do they workout as;
  • Y2 – 4y
  • +2y -8
  • We need to collect the terms
  • -4y + 2y = -2y
  • So the equation is y2 -2y -8
try these6
Try these
  • (s+1)(3s+2)
  • (2+f)(1+4f)
  • (d-2)(3d+5)
  • (7+k)(1+k)
  • (a+3)(4a-1)
  • (y-2)(y+2)
  • (a+b)(a-b)
answers9
Answers
  • 3s2+5s+2
  • 2+9f+4f2
  • 3d2-d-10
  • 7+8k+k2
  • 4a2+11a-3
  • Y2-4
  • A2-b2
brackets 2
(Brackets)2
  • If you have (4g+h)2
  • This means (4g+h) )(4g+h)
  • First we …
  • Split up the first bracket
  • 4g(4g+h)
  • +h(4g+h)

2. Then we multiply this out

  • 16g2 + 4gh
  • +4gh + h2

3. Then we collect terms

  • +4gh + 4gh = +8gh
  • So our equation is
  • 16g2 + 8gh + h2
solving equations
Solving Equations
  • If you have a number and no x2 or x3 you can solve a linear equation
  • E.g.
  • 4x=16
  • X = 16/4
  • X= 4
  • x/7=-2
  • Multiply both sides by 7
  • X = -14
  • What you do to one side of the equals sign you must do to the other to keep everything balanced
try these7
Try these
  • x/5= 12
  • X-7=23
  • X + 12 = 45
  • 0.5x=3
  • 2x/3 = -6
  • x/3 + 2 =10
  • 7x= x + 42
  • 2.5x = 1.5x + 6
answers10
Answers
  • X= 60
  • X= 30
  • X= 33
  • X= 6
  • X= -9
  • X= 24
  • X= 7
  • X= 6
solving equations1
Solving Equations
  • You should always try to keep x positive, so work from the side with the most x’s
  • E.g.
  • 2x + 17= 4x
  • We need to take 2x away from both sides
  • 17 = 2x
  • 8.5 = x
harder questions
Harder questions
  • 13x-15 = 12x+19
  • 2.5x + 10 = 1.5x + 17
  • 12x-1 = 7x+19
  • 4x-3 = 12-x
  • 2x-7 = 3 – 8x
  • 3(2x+2) = 24
  • 6(3x+1) = 3(4x+6)
  • 10(3x-4) = 5(6-x)
answers11
Answers
  • X= 34
  • X= 7
  • X= 4
  • X= 3
  • X= 1
  • X= 3
  • X= 1
  • X= 2
changing the subject
Changing the Subject
  • Sometimes you have to rearrange equations
  • E.g.
  • C= a – b
  • I want to find out what a equals
  • If I add b to both sides I have a on it’s own
  • C + b = a
try these8
Try these
  • T= sk - h
  • V=u + at
  • M=k + nk
  • T2 = 7r + x/4
  • H= y/4
  • T= s2 + 5
  • A=πr2
  • S= ½gt2
answers12
Answers
  • T/s + h/s = k
  • v/a – u/a = t
  • m/k– k/k = n
  • T2/7- x/4/7 = r
  • 4h = y
  • √t-5 = s
  • √a/ π = r
  • √2s/g= t