Factorise the expression `-12y^2+18y-6` (2 marks)
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Factorise the expression `-12y^2+18y-6` (2 marks)
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`6(2y-1)(1-y)\ \ text(or)\ \ 6(1-2y)(y-1)`
`-12y^2+18y-6=-6(2y^2-3y+1)`
`-6(2y^2-3y+1)=>\ \ ` | `text{P}` | `=2xx1=2` |
`text{S}` | `=-3` | |
`text{F}` | `=-2,-1` |
`-6(2y^2-3y+1)` | `=(-6(2y-1)(2y-2))/2` |
`=-6(2y-1)(y-1)` | |
`=6(2y-1)(1-y)\ \ text(or)\ \ 6(1-2y)(y-1)` |
Fully factorise the expression `6y^2+10y-4` (2 marks)
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`2(3y-1)(y+2)`
`6y^2+10y-4=2(3y^2+5y-2)`
`2(3y^2+5y-2)=>\ \ ` | `text{P}` | `=3xx-2=-6` |
`text{S}` | `=5` | |
`text{F}` | `=-1,6` |
`2(3y^2+5y-2)` | `=(2(3y-1)(3y+6))/3` |
`=2(3y-1)(y+2)` |
Factorise the expression `2x^2+x-6` (2 marks)
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`(2x-3)(x+2)`
`2x^2+x-6=>\ \ ` | `text{P}` | `=2xx-6=-12` |
`text{S}` | `=1` | |
`text{F}` | `=-3,4` |
`2x^2+x-6` | `=((2x-3)(2x+4))/2` |
`=(2x-3)(x+2)` |
Fully factorise the expression `3a^2+12ab-2a-8b` (2 marks)
`(3a-2)(a+4b)`
`3a^2+12ab-2a-8b` | `=3a(a+4b)-2(a+4b)` | |
`=(3a-2)(a+4b)` |
Fully factorise the expression `2x^2-6xy-3x+9y` (2 marks)
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`(2x-3)(x-3y)`
`2x^2-6xy-3x+9y` | `=2x(x-3y)-3(x-3y)` | |
`=(2x-3)(x-3y)` |
Factorise the expression `5b^3-5b` (2 marks)
`5b(b+1)(b-1)`
`5b^3-5b` | `=5b(b^2-1)` | |
`=5b(b+1)(b-1)` |
Expand and simplify the expression `(a+b)^2-(a-b)^2` (2 marks)
`4ab`
`(a+b)^2-(a-b)^2` | `=a^2+2ab+b^2-(a^2-2ab+b^2)` | |
`=a^2+2ab+b^2-a^2+2ab-b^2` | ||
`=4ab` |
Expand and simplify the expression `(4-7x)^2` (2 marks)
`49x^2-56x+16`
`(4-7x)^2` | `=(4-7x)(4-7x)` | |
`=16-28x-28x+49x^2` | ||
`=49x^2-56x+16` |
Expand and simplify the expression `(c-2)^2` (2 marks)
`c^2-4c+4`
`(c-2)^2` | `=(c-2)(c-2)` | |
`=c^2-2c-2c+4` | ||
`=c^2-4c+4` |
Expand and simplify the expression `(2x-5)^2` (2 marks)
`4x^2-20x+25`
`(2x-5)^2` | `=(2x-5)(2x-5)` | |
`=4x^2-10x-10x+25` | ||
`=4x^2-20x+25` |
Expand and simplify the expression `(2y-3)(2y+3)` (2 marks)
`4y^2-9`
`(2y-3)(2y+3)` | `=4y^2+6y-6y-9` | |
`=4y^2-9` |
Expand and simplify the expression `(p-4q)(p+4q)` (2 marks)
`p^2-16q^2`
`(p-4q)(p+4q)` | `=p^2+4pq-4pq-16q^2` | |
`=p^2-16q^2` |
Expand and simplify the expression `(3a+1)(2-a)+2a+4` (2 marks)
`-3a^2+7a+6`
`(3a+1)(2-a)+2a+4` | `=6a-3a^2+2-a+2a+4` | |
`=-3a^2+7a+6` |
Factorise the expression `b^2+4b-12` (2 marks)
`(b+6)(b-2)`
`b^2+4b-12=(b+6)(b-2)`
Factorise the expression `-a^2+3a+10` (2 marks)
`-(a+2)(a-5)\ \ text(or)\ \ (5-a)(a+2)`
`-a^2+3a+10` | `=-(a^2-3a-10)` | |
`=-(a-5)(a+2)` | ||
`=(5-a)(a+2)` |
Factorise the expression `n^2+5n-24` (2 marks)
`(n+8)(n-3)`
`n^2+5n-24=(n+8)(n-3)`
Fully factorise the expression `6x^2-8x-8` (2 marks)
`2(3x+2)(x-2)`
`6x^2-8x-8=2(3x+2)(x-2)`
Factorise the expression `2p^2-5p-12` (2 marks)
`(2p+3)(p-4)`
`2p^2-5p-12=(2p+3)(p-4)`
Factorise the expression `y^2-2y-15` (2 marks)
`(y+3)(y-5)`
`y^2-2y-15=(y+3)(y-5)`
Factorise the expression `x^2+6x+8` (2 marks)
`(x+2)(x+4)`
`x^2+6x+8=(x+2)(x+4)`
Expand and simplify the expression `(4x-3y)(y-x)` (2 marks)
`-4x^2+7xy-3y^2`
`(4x-3y)(y-x)` | `=4xy-4x^2-3y^2+3xy` | |
`=-4x^2+7xy-3y^2` |
Expand and simplify the expression `(7m-3)(m-2)` (2 marks)
`7m^2-17m+6`
`(7m-3)(m-2)` | `=7m^2-14m-3m+6` | |
`=7m^2-17m+6` |
Expand and simplify the expression `(a-b)(3a-2b)` (2 marks)
`3a^2-5ab+2b^2`
`(a-b)(3a-2b)` | `=3a^2-2ab-3ab+2b^2` | |
`=3a^2-5ab+2b^2` |
Expand and simplify the expression `(2p-3)(p+1)` (2 marks)
`2p^2-p-3`
`(2p-3)(p+1)` | `=2p^2+2p-3p-3` | |
`=2p^2-p-3` |
Expand and simplify the expression `(2x-1)(2x+1)` (2 marks)
`4x^2-1`
`(2x-1)(2x+1)` | `=4x^2+2x-2x-1` | |
`=4x^2-1` |
Expand and simplify the expression
`13-3(x-4)` (2 marks)
`25-3x`
`13-3(x-4)` | `=13-3x+12` | |
`=25-3x` |
Expand and simplify the expression
`3a(4a-5)-2(a-3)` (2 marks)
`12a^2-17a+6`
`3a(4a-5)-2(a-3)` | `=12a^2-15a-2a+6` | |
`=12a^2-17a+6` |
Expand the expression `-2(5x^2-3x-4)` (2 marks)
`-10x^2+6x+8`
`-2(5x^2-3x-4)=-10x^2+6x+8`
Expand the expression `3(2y^2-3y+1)` (2 marks)
`6y^2-9y+3`
`3(2y^2-3y+1)=6y^2-9y+3`
Expand and simplify the expression `4a(a-3)-5(6-a)` (2 marks)
`4a^2-7a-30`
`4a(a-3)-5(6-a)` | `=4a^2-12a-30+5a` | |
`=4a^2-7a-30` |
Expand and simplify the expression `3x(x-2)+4(x-5)` (2 marks)
`3x^2-2x-20`
`3x(x-2)+4(x-5)` | `=3x^2-6x+4x-20` | |
`=3x^2-2x-20` |
Which of the following is always equal to `a-b`?
`D`
`a-b = -b + a`
`=>D`
Which expression is equivalent to `4x^2-12x + x^3?`
`D`
`x (4x-12 + x^2)`
`= 4x^2-12x + x^3`
`=>D`
What expression is equivalent to `-(y-6)`?
`D`
`-(y-6) = -y-(-6)=-y + 6`
`=>D`
Which expression is equal to `4x-8 + 3x + 2`?
`B`
`4x-8 + 3x + 2=7x-6`
`=>B`
Which expression is equivalent to `12x + 24`?
`A`
`3 (4x + 8)` | `= 3 xx 4x + 3 xx 8` |
`= 12x + 24` |
`=>A`
Which expression is equivalent to `5-6t`?
`D`
`-6t+5`
`=>D`
Which one of the following expressions is equivalent to `4 (3m-1)`?
`C`
`4 (3m-1)`
`= (4 xx 3m)-(4 xx 1)`
`= 12m-4`
`=>C`
The expression `3x + 7 + 8x + 11` can also be written as
`B`
`3x + 7 + 8x + 11 = 11x + 18`
`=>B`
Which expression is equivalent to `2(3x-4) + 2`?
`C`
`2(3x-4) + 2`
`= 6x-8 + 2`
`= 6x-6`
`=> C`
Which of the following is `4x + 3y-x-5y` in its simplest form?
`A`
`4x + 3y-x-5y`
`= 3x-2y`
`⇒ A`
Simplify `5-2(x + 7)`. (2 marks)
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`-2x-9`
`5-2(x + 7)` | `= 5-2x-14` |
`= -2x-9` |