Algebra

• What do index laws state about powers with the same base when multiplied?

  The powers can be added together.
• How do you simplify $x^7 / x^2$ using index laws?


  You subtract the powers to get $x^{5}$.
• What is the result of $(x^2)^5$ using index laws?


  The result is $x^{10}$.
• How do you simplify the expression $\frac{30x^2y^3}{6xy^2}$?


  The simplified expression is $5xy$.
• What is $2^3$ equal to?


  It is equal to 8.
• What happens to the powers of $x$ and $y$ when $2(x^2y)^3$ is expanded?


  The powers become $x^6$ and $y^3$.
• What is the process for expanding brackets like $B(3B + 7)$?


  • Multiply $B$ by $3B$ to get $3B^2$
  • Multiply $B$ by $7$ to get $7B$
  • Combine to get $3B^2 +$$7B$
• How do you expand $3y(5 - 2y)$?


  You get $15y - 6y^2$.
• What are the steps to expand and simplify $3(5x + 4) - 2(3x - 2)$?


  1. Expand: $15x +$$12 - 6x +$$4$
  2. Combine like terms: $9x +$$16$
• What is the result of expanding $(x - 5)(x + 3)$?


  The result is $x^2 - 2x - 15$.
• How do you factor $3x +$$15$?


  • Factor out $3$: $3(x + 5)$
• What is the process for fully factorizing $35x +$$21x^2$?


  1. Identify common factors: $7x$
  2. Factor out: $7x(5 + 3x)$
• How do you factor a quadratic like $x^2 +$$7x +$$12$?


  You find factors that multiply to 12 and add to 7, which are 3 and 4.
• What is the factorization of $x^2 - 3x - 28$?


  The factorization is $(x + 4)(x - 7)$.
• How do you solve the equation $3x +$$5 =$$26$?


  You subtract 5 from both sides and then divide by 3 to find $x =$$7$.
• What is the solution to $5x - 2 =$$21$?


  The solution is $x =$$\frac{23}{5}$.
• How do you solve for $x</text> in the equation <latex>5x - 3 =$$9$?


  You add 3 to both sides and then divide by 5 to find $x =$$\frac{12}{5}$.
• What is the process for making $x$ the subject in the equation $y =$$3x +$$5$?


  1. Subtract 5 from both sides: $y - 5 =$$3x$
  2. Divide by 3: $x =$$\frac{y - 5}{3}$
• How do you make $x$ the subject in the equation $y =$$\frac{x + 5}{3}$?


  1. Multiply by 3: $3y =$$x +$$5$
  2. Subtract 5: $x =$$3y - 5$
• How do you find the value of $a$ in the equation $a =$$5b +$$2c$ when $b =$$3$ and $c =$$-2$?


  You substitute to get $a =$$5(3) +$$2(-2) =$$11$.
• What is the process for solving simultaneous equations?

  1. Make coefficients of one variable the same.
  2. Add or subtract equations to eliminate one variable.
  3. Solve for the remaining variable.
  4. Substitute back to find the other variable.
• How do you make the coefficients of $y</text> the same in the equations <latex>y =$$3x +$$5$ and $y =$$5x - 2$?


  You can multiply the first equation by 3 to match the coefficient of <latex>y</text>.
• What should you always do when substituting numbers into equations?

  Put them into brackets
• What is the goal when solving simultaneous equations?

  To make the coefficients of one variable the same
• How do you make the coefficient of Y the same in the equations given?

  Multiply the first equation by 3
• What happens when you add the two equations after adjusting the coefficients?

  The Y terms cancel out
• What is the result of adding the two adjusted equations together?

  13x = 91
• What is the value of x after solving the equation 13x = 91?

  x = 7
• What must you do after finding the value of x in simultaneous equations?

  Substitute x back into one of the original equations
• If x = 7, what is the equation used to find y using equation 1?

  4(7) + y = 25
• What is the final value of y after solving the equation 4(7) + y = 25?

  y = -3
• What is the relationship between the ages of Adam, Brian, and Chris?

  Adam is 8 years older than Chris, and Brian is twice as old as Adam
• If Chris's age is represented by x, how can Adam's age be expressed?

  x + 8
• How can Brian's age be expressed in terms of x?

  2(x + 8)
• What equation represents the sum of their ages being 92?

  x + (x + 8) + 2(x + 8) = 92
• What is the simplified form of the equation x + (x + 8) + 2(x + 8) = 92?

  4x + 24 = 92
• What is the value of x after solving the equation 4x + 24 = 92?

  x = 17
• How old is Adam if Chris is 17?

  25
• How old is Brian if Adam is 25?

  50
• What is the expression for the perimeter of the quadrilateral?

  8x - 4