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Given x=4, y=3, z=2 and p=6, q=2p, r=q+p, evaluate the following expressions: a) x2 - y, b) xy + 2z, c) 2x + yz + y2, d) (xy)2 + yz - z, e) p+q+r

Mathematics

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WEDNESDAY

1. Evaluate: If x=4x=4, y=3y=3, and z=2z=2, determine the value of:

a) x2−yx^2 - y

  1. Substitute the given values into the expression.

    x2−y=(4)2−3x^2 - y = (4)^2 - 3
  2. Calculate the square.

    16−316 - 3
  3. Perform the subtraction.

    1313

    The value is 13\boxed{13}.

    b) xy+2zxy + 2z

  4. Substitute the given values into the expression.

    xy+2z=(4)(3)+2(2)xy + 2z = (4)(3) + 2(2)
  5. Perform the multiplications.

    12+412 + 4
  6. Perform the addition.

    1616

    The value is 16\boxed{16}.

    c) 2x+yz+y22x + yz + y^2

  7. Substitute the given values into the expression.

    2x+yz+y2=2(4)+(3)(2)+(3)22x + yz + y^2 = 2(4) + (3)(2) + (3)^2
  8. Perform the multiplications and the square.

    8+6+98 + 6 + 9
  9. Perform the additions.

    14+9=2314 + 9 = 23

    The value is 23\boxed{23}.

    d) (xy)2+yz−z(xy)^2 + yz - z

  10. Substitute the given values into the expression.

    (xy)2+yz−z=((4)(3))2+(3)(2)−2(xy)^2 + yz - z = ((4)(3))^2 + (3)(2) - 2
  11. Perform the multiplication inside the parenthesis first.

    (12)2+6−2(12)^2 + 6 - 2
  12. Calculate the square.

    144+6−2144 + 6 - 2
  13. Perform the additions and subtractions from left to right.

    150−2=148150 - 2 = 148

    The value is 148\boxed{148}.

    2. If p=6p=6, q=2pq=2p, and r=q+pr=q+p, what is the value of:

  14. Calculate the values of qq and rr.

    q=2p=2(6)=12q = 2p = 2(6) = 12 r=q+p=12+6=18r = q + p = 12 + 6 = 18

    So, p=6p=6, q=12q=12, r=18r=18.

    a) p+q+rp + q + r

  15. Substitute the calculated values into the expression.

    p+q+r=6+12+18p + q + r = 6 + 12 + 18
  16. Perform the additions.

    18+18=3618 + 18 = 36

    The value is 36\boxed{36}.

    b) p(q−r)p(q - r)

  17. Substitute the calculated values into the expression.

    p(q−r)=6(12−18)p(q - r) = 6(12 - 18)
  18. Perform the subtraction inside the parenthesis.

    6(−6)6(-6)
  19. Perform the multiplication.

    −36-36

    The value is −36\boxed{-36}.

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