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Show that the distributive property of multiplication over addition holds true for the given values: a (b + c) = (a b) + (a * c)

Mathematics

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2 parts
d
-22
f
-7

Step-by-step solution

31 steps

here are the calculations:

Part a· 6 steps

a×(b+c)a \times (b+c) if a=2,b=−3,c=−5a=2, b=-3, c=-5

We will show that a×(b+c)=(a×b)+(a×c)a \times (b+c) = (a \times b) + (a \times c).

Left side: a×(b+c)a \times (b+c)

  1. Substitute the given values.

    2×((−3)+(−5))2 \times ((-3) + (-5))

  2. Perform the addition inside the parenthesis.

    2×(−8)2 \times (-8)

  3. Perform the multiplication.

    −16-16

    Right side: (a×b)+(a×c)(a \times b) + (a \times c)

  4. Substitute the given values.

    (2×(−3))+(2×(−5))(2 \times (-3)) + (2 \times (-5))

  5. Perform the multiplications.

    −6+(−10)-6 + (-10)

  6. Perform the addition.

    −16-16

    Since −16=−16-16 = -16, the property holds.

Part b· 6 steps

a×(b+c)a \times (b+c) if a=−7,b=2,c=3a=-7, b=2, c=3

We will show that a×(b+c)=(a×b)+(a×c)a \times (b+c) = (a \times b) + (a \times c).

Left side: a×(b+c)a \times (b+c)

  1. Substitute the given values.

    −7×(2+3)-7 \times (2 + 3)

  2. Perform the addition inside the parenthesis.

    −7×5-7 \times 5

  3. Perform the multiplication.

    −35-35

    Right side: (a×b)+(a×c)(a \times b) + (a \times c)

  4. Substitute the given values.

    (−7×2)+(−7×3)(-7 \times 2) + (-7 \times 3)

  5. Perform the multiplications.

    −14+(−21)-14 + (-21)

  6. Perform the addition.

    −35-35

    Since −35=−35-35 = -35, the property holds.

Part c· 6 steps

a×(b+c)a \times (b+c) if a=1,b=−8,c=2a=1, b=-8, c=2

We will show that a×(b+c)=(a×b)+(a×c)a \times (b+c) = (a \times b) + (a \times c).

Left side: a×(b+c)a \times (b+c)

  1. Substitute the given values.

    1×((−8)+2)1 \times ((-8) + 2)

  2. Perform the addition inside the parenthesis.

    1×(−6)1 \times (-6)

  3. Perform the multiplication.

    −6-6

    Right side: (a×b)+(a×c)(a \times b) + (a \times c)

  4. Substitute the given values.

    (1×(−8))+(1×2)(1 \times (-8)) + (1 \times 2)

  5. Perform the multiplications.

    −8+2-8 + 2

  6. Perform the addition.

    −6-6

    Since −6=−6-6 = -6, the property holds.

Part d-22

(a×b)+a+c(a \times b) + a + c if a=3,b=−10,c=5a=3, b=-10, c=5

  1. Substitute the given values into the expression.

    (3×(−10))+3+5(3 \times (-10)) + 3 + 5

  2. Perform the multiplication.

    −30+3+5-30 + 3 + 5

  3. Perform the additions from left to right.

    −27+5-27 + 5

  4. Perform the final addition.

    −22\boxed{-22}

Part e· 6 steps

m×(n+p)m \times (n+p) if m=3,n=2,p=−11m=3, n=2, p=-11

We will show that m×(n+p)=(m×n)+(m×p)m \times (n+p) = (m \times n) + (m \times p).

Left side: m×(n+p)m \times (n+p)

  1. Substitute the given values.

    3×(2+(−11))3 \times (2 + (-11))

  2. Perform the addition inside the parenthesis.

    3×(−9)3 \times (-9)

  3. Perform the multiplication.

    −27-27

    Right side: (m×n)+(m×p)(m \times n) + (m \times p)

  4. Substitute the given values.

    (3×2)+(3×(−11))(3 \times 2) + (3 \times (-11))

  5. Perform the multiplications.

    6+(−33)6 + (-33)

  6. Perform the addition.

    −27-27

    Since −27=−27-27 = -27, the property holds.

Part f-7

(m×n)+(m×p)(m \times n) + (m \times p) if m=7,n=8,p=−9m=7, n=8, p=-9

  1. Substitute the given values into the expression.

    (7×8)+(7×(−9))(7 \times 8) + (7 \times (-9))

  2. Perform the multiplications.

    56+(−63)56 + (-63)

  3. Perform the addition.

    −7\boxed{-7}
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