Tag: order operations and algebra

Questions Related to order operations and algebra

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

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

  1. $-9x-12$

  2. $-9x-4x^2$

  3. $-9x-5$

  4. $-4x-5$

Show answer
Correct Option: C
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.
$=$ $4-x^2\div x +(4\times-(\dfrac{2x^3}{x^2}))-3^2$
$=$ $4-x+(4\times -2x)-9$
$=$ $4-x-8x-9$
$=$ $-9x-5$

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

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

  1. $x^3+199x^2-x+1$

  2. $2x^3+199x^2-x+1$

  3. $2x^3-199x^2-x+1$

  4. $2x^3+199x^2-x-1$

Show answer
Correct Option: B
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.
$=$ $[((100+x)x^4)\div x^2]\times 2 - (x+x^2-1)$
$=$ $\dfrac{(100+x)(x^4)}{x^2}\times 2-x-x^2+1$
$=$ $200x^2+2x^3-x-x^2+1$
$=$ $2x^3+199x^2-x+1$

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

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

  1. $x^3+2x^2-x-2$

  2. $x^3-2x^2-x-2$

  3. $-x^3+2x^2-x-2$

  4. $x^3+2x^2+x-+$

Show answer
Correct Option: A
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.
$=$ $\frac{x-1(x^2+x-2)(x+1)(x-1)}{(x-1(x-1)}$
$=$ $x^3+x^2-2x+x^2+x-2$
$=$ $x^3+2x^2-x-2$

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

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

  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. $8x^2+2y^2-4xy^2-8x+22y+10$

Show answer
Correct Option: C
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.
$=$ $12-[5y+2xy^2-4x^2+4x+6y-y^2+1]\times 2$
$=$ $12- [2xy^2-4x^2+4x+11y-y^2+1]\times 2$
$=$ $12-[4xy^2-8x^2+8x+22y-2y^2+2]$
$=$ $12-4xy^2+8x^2-8x-22y+2y^2-2$
$=$ $8x^2+2y^2-4xy^2-8x-22y+10$

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

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

  1. $x^3-x^2-2x$

  2. $-x^3-x^2-2x$

  3. $x^3-x^2+2x$

  4. $x^3+x^2+2x$

Show answer
Correct Option: A
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.
$=$ $-2x^2-x[\dfrac{(-x)(-2+x)}{x}]+x^3$
$=$ $-2x^2-x[2-x]+x^3$
$=$ $x^3-2x^2-2x+x^2$
$=$ $x^3-x^2-2x$

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

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

  1. $10y^4+11y^2+y$

  2. $-10y^4+11y^2-y$

  3. $-10y^4+11y^2+y$

  4. $-10y^4-11y^2+y$

Show answer
Correct Option: C
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.
$=$ $2y-y+y^2+5y[-2y^3+2y]$
$=$ $y+y^2-10y^4+10y^2$
$=$ $-10y^4+11y^2+y$

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

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

  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. $-4x^5+12x^4-3x^3+x^2$

Show answer
Correct Option: D
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.
$=$ $4x^3[(3x-x^2)-1]+(x^2)[x+1]$
$=$ $4x^3[3x-x^2-1]+x^3+x^2$
$=$ $12x^4-4x^5-4x^3+x^3+x^2$
$=$ $-4x^5+12x^4-3x^3+x^2$

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

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

  1. $15x^{12}-12x-4$

  2. $15x^4-12x-4$

  3. $15x^4+12x-4$

  4. $5x^4-12x-4$

Show answer
Correct Option: B
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.
$=$ $5x[2x(x^2+x^3)-x^3]-4x^2\div x^2-12x$
$=$ $5x[2x^3+2x^4-x^3]-\dfrac{4x^2}{x^2}-12x$
$=$ $5x[x^3+2x^4]-4-12x$
$=$ $5x^4+10x^4-12x-4$
$=$ $15x^4-12x-4$

Use the BODMAS rule to simplify the expression: 

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

  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. $-x^4+4x^3-x^2+xy^2$

Show answer
Correct Option: D
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.
$=$ $xy^2+x^3+[-x^3+x^2]2x+x^3-x^2$
$=$ $xy^2+x^3-x^4+2x^3+x^3-x^2$
$=$ $xy^2+4x^3-x^4-x^2$
$=$ $-x^4+4x^3-x^2+xy^2$

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

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

  1. $x^3+7x^2+8x+1$

  2. $x^3-7x^2+8x-1$

  3. $x^3+7x^2+8x-1$

  4. $x^3+7x^2-8x-1$

Show answer
Correct Option: C
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.
$=$ $x^2\times(x-1)+[(2x+2)\times 4x]-1$
$=$ $x^3-x^2+8x^2+8x-1$
$=$ $x^3+7x^2+8x-1$