Tag: using brackets in algebraic expressions

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Questions Related to using brackets in algebraic expressions

Multiple choice maths brackets order operations and algebra using brackets in algebraic expressions order of operations

Find the value of the expression using BODMAS rule: $4-x^2\div x +(4\times-(\dfrac{2x^3}{x^2}))-3^2$.

  1. $-9x-12$
  2. $-9x-4x^2$
  3. $-9x-5$
  4. $-4x-5$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$4-x^2\div x +(4\times-(\dfrac{2x^3}{x^2}))-3^2$
We need to follow BODMAS rule.
=> Brackets (parts of a calculation inside brackets always come first).
=> Orders (numbers involving powers or square roots).
=> Division.
=> Multiplication.
=> Addition.
=> Subtraction.
$=$ $4-x^2\div x +(4\times-(\dfrac{2x^3}{x^2}))-3^2$
$=$ $4-x+(4\times -2x)-9$
$=$ $4-x-8x-9$
$=$ $-9x-5$

Multiple choice maths brackets order operations and algebra using brackets in algebraic expressions order of operations

Simplify using BODMAS rule: $[((100+x)x^4)\div x^2]\times 2 - (x+x^2-1)$.

  1. $x^3+199x^2-x+1$
  2. $2x^3+199x^2-x+1$
  3. $2x^3-199x^2-x+1$
  4. $2x^3+199x^2-x-1$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$[((100+x)x^4)\div x^2]\times 2 - (x+x^2-1)$
We need to follow BODMAS rule.
=> Brackets (parts of a calculation inside brackets always come first).
=> Orders (numbers involving powers or square roots).
=> Division.
=> Multiplication.
=> Addition.
=> Subtraction.
$=$ $[((100+x)x^4)\div x^2]\times 2 - (x+x^2-1)$
$=$ $\dfrac{(100+x)(x^4)}{x^2}\times 2-x-x^2+1$
$=$ $200x^2+2x^3-x-x^2+1$
$=$ $2x^3+199x^2-x+1$

Multiple choice maths brackets order operations and algebra using brackets in algebraic expressions order of operations

Use the BODMAS rule to reduce the expression: $x-1[(x^2+x-2)(x^2-1^2)\div (x-1)^2]$.

  1. $x^3+2x^2-x-2$
  2. $x^3-2x^2-x-2$
  3. $-x^3+2x^2-x-2$
  4. $x^3+2x^2+x-+$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$x-1[(x^2+x-2)(x^2-1^2)\div (x-1)^2]$
We need to follow BODMAS rule.
=> Brackets (parts of a calculation inside brackets always come first).
=> Orders (numbers involving powers or square roots).
=> Division.
=> Multiplication.
=> Addition.
=> Subtraction.
$=$ $\frac{x-1(x^2+x-2)(x+1)(x-1)}{(x-1(x-1)}$
$=$ $x^3+x^2-2x+x^2+x-2$
$=$ $x^3+2x^2-x-2$

Multiple choice maths brackets order operations and algebra using brackets in algebraic expressions order of operations

Solve: $12-[5y+2x(y^2-2x+2)+6y-(y^2-1)]\times 2$.

  1. $8x^2+y^2-4xy^2-8x-22y+10$
  2. $8x^2+2y^2+4xy^2-8x-22y+10$
  3. $8x^2+2y^2-4xy^2-8x-22y+10$
  4. $8x^2+2y^2-4xy^2-8x+22y+10$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$12-[5y+2x(y^2-2x+2)+6y-(y^2-1)]\times 0.1$
We need to follow BODMAS rule.
=> Brackets (parts of a calculation inside brackets always come first).
=> Orders (numbers involving powers or square roots).
=> Division.
=> Multiplication.
=> Addition.
=> Subtraction.
$=$ $12-[5y+2xy^2-4x^2+4x+6y-y^2+1]\times 2$
$=$ $12- [2xy^2-4x^2+4x+11y-y^2+1]\times 2$
$=$ $12-[4xy^2-8x^2+8x+22y-2y^2+2]$
$=$ $12-4xy^2+8x^2-8x-22y+2y^2-2$
$=$ $8x^2+2y^2-4xy^2-8x-22y+10$

Multiple choice maths brackets order operations and algebra using brackets in algebraic expressions order of operations

Expand the expression using BODMAS rule: $x^2-x[(-x)(-2+x)]\div x+x^3-3x^2$

  1. $x^3-x^2-2x$
  2. $-x^3-x^2-2x$
  3. $x^3-x^2+2x$
  4. $x^3+x^2+2x$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$x^2-x[(-x)(-2+x)]\div x+x^3-3x^2$
We need to follow BODMAS rule.
=> Brackets (parts of a calculation inside brackets always come first).
=> Orders (numbers involving powers or square roots).
=> Division.
=> Multiplication.
=> Addition.
=> Subtraction.
$=$ $-2x^2-x[\dfrac{(-x)(-2+x)}{x}]+x^3$
$=$ $-2x^2-x[2-x]+x^3$
$=$ $x^3-2x^2-2x+x^2$
$=$ $x^3-x^2-2x$

Multiple choice maths brackets order operations and algebra using brackets in algebraic expressions order of operations

Reduce the following expression using BODMAS rule: $2y-1(y-y^2)+5y[(-2y)(y^2-1)]$

  1. $10y^4+11y^2+y$
  2. $-10y^4+11y^2-y$
  3. $-10y^4+11y^2+y$
  4. $-10y^4-11y^2+y$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$2y-1(y-y^2)+5y[(-2y)(y^2-1)]$
We need to follow BODMAS rule.
=> Brackets (parts of a calculation inside brackets always come first).
=> Orders (numbers involving powers or square roots).
=> Division.
=> Multiplication.
=> Addition.
=> Subtraction.
$=$ $2y-y+y^2+5y[-2y^3+2y]$
$=$ $y+y^2-10y^4+10y^2$
$=$ $-10y^4+11y^2+y$

Multiple choice maths brackets order operations and algebra using brackets in algebraic expressions order of operations

Simplify the expression: $4x^3[(3x-x^2)-1]+(x^2)[x+1]$.

  1. $-4x^5-12x^4-3x^3+x^2$
  2. $-4x^5+12x^4+3x^3+x^2$
  3. $-4x^5+12x^4-3x^3-x^2$
  4. $-4x^5+12x^4-3x^3+x^2$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

$4x^3[(3x-x^2)-1]+(x^2)[x+1]$
We need to follow BODMAS rule.
=> Brackets (parts of a calculation inside brackets always come first).
=> Orders (numbers involving powers or square roots).
=> Division.
=> Multiplication.
=> Addition.
=> Subtraction.
$=$ $4x^3[(3x-x^2)-1]+(x^2)[x+1]$
$=$ $4x^3[3x-x^2-1]+x^3+x^2$
$=$ $12x^4-4x^5-4x^3+x^3+x^2$
$=$ $-4x^5+12x^4-3x^3+x^2$

Multiple choice maths brackets order operations and algebra using brackets in algebraic expressions order of operations

Find the value of $5x[2x(x^2+x^3)-x^3]-4x^2\div x^2-12x$.

  1. $15x^{12}-12x-4$
  2. $15x^4-12x-4$
  3. $15x^4+12x-4$
  4. $5x^4-12x-4$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$5x[2x(x^2+x^3)-x^3]-4x^2\div x^2-12x$
We need to follow BODMAS rule.
=> Brackets (parts of a calculation inside brackets always come first).
=> Orders (numbers involving powers or square roots).
=> Division.
=> Multiplication.
=> Addition.
=> Subtraction.
$=$ $5x[2x(x^2+x^3)-x^3]-4x^2\div x^2-12x$
$=$ $5x[2x^3+2x^4-x^3]-\dfrac{4x^2}{x^2}-12x$
$=$ $5x[x^3+2x^4]-4-12x$
$=$ $5x^4+10x^4-12x-4$
$=$ $15x^4-12x-4$

Multiple choice maths brackets order operations and algebra using brackets in algebraic expressions order of operations

Use the BODMAS rule to simplify the expression: 

  1. $-x^4-4x^3-x^2+xy^2$
  2. $-x^4+4x^2-x^2+xy^2$
  3. $-x^4+4x^3+x^2+xy^2$
  4. $-x^4+4x^3-x^2+xy^2$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

$xy^2+x^3-x[x^2-x][2x]+(x-1)x^2$
We need to follow BODMAS rule.
=> Brackets (parts of a calculation inside brackets always come first).
=> Orders (numbers involving powers or square roots).
=> Division.
=> Multiplication.
=> Addition.
=> Subtraction.
$=$ $xy^2+x^3+[-x^3+x^2]2x+x^3-x^2$
$=$ $xy^2+x^3-x^4+2x^3+x^3-x^2$
$=$ $xy^2+4x^3-x^4-x^2$
$=$ $-x^4+4x^3-x^2+xy^2$

Multiple choice maths brackets order operations and algebra using brackets in algebraic expressions order of operations

Simplify the expression: $x^2\times(x-1)+[(2x+2)\times 4x]-1$

  1. $x^3+7x^2+8x+1$
  2. $x^3-7x^2+8x-1$
  3. $x^3+7x^2+8x-1$
  4. $x^3+7x^2-8x-1$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$x^2\times(x-1)+[(2x+2)\times 4x]-1$
We need to follow BODMAS rule.
=> Brackets (parts of a calculation inside brackets always come first).
=> Orders (numbers involving powers or square roots).
=> Division.
=> Multiplication.
=> Addition.
=> Subtraction.
$=$ $x^2\times(x-1)+[(2x+2)\times 4x]-1$
$=$ $x^3-x^2+8x^2+8x-1$
$=$ $x^3+7x^2+8x-1$