This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
You're on a roll — here are the calculations: *a) a × (b+c) if a=2, b=-3, c=-5 We will show that a × (b+c) = (a × b) + (a × c). Left side: a × (b+c) Step 1: Substitute the given values. 2 × ((-3) + (-5)) Step 2: Perform the addition inside the parenthesis. 2 × (-8) Step 3: Perform the multiplication. -16 Right side: (a × b) + (a × c) Step 1: Substitute the given values. (2 × (-3)) + (2 × (-5)) Step 2: Perform the multiplications. -6 + (-10) Step 3: Perform the addition. -16 Since -16 = -16, the property holds. *b) a × (b+c) if a=-7, b=2, c=3 We will show that a × (b+c) = (a × b) + (a × c). Left side: a × (b+c) Step 1: Substitute the given values. -7 × (2 + 3) Step 2: Perform the addition inside the parenthesis. -7 × 5 Step 3: Perform the multiplication. -35 Right side: (a × b) + (a × c) Step 1: Substitute the given values. (-7 × 2) + (-7 × 3) Step 2: Perform the multiplications. -14 + (-21) Step 3: Perform the addition. -35 Since -35 = -35, the property holds. *c) a × (b+c) if a=1, b=-8, c=2 We will show that a × (b+c) = (a × b) + (a × c). Left side: a × (b+c) Step 1: Substitute the given values. 1 × ((-8) + 2) Step 2: Perform the addition inside the parenthesis. 1 × (-6) Step 3: Perform the multiplication. -6 Right side: (a × b) + (a × c) Step 1: Substitute the given values. (1 × (-8)) + (1 × 2) Step 2: Perform the multiplications. -8 + 2 Step 3: Perform the addition. -6 Since -6 = -6, the property holds. *d) (a × b) + a + c if a=3, b=-10, c=5 Step 1: Substitute the given values into the expression. (3 × (-10)) + 3 + 5 Step 2: Perform the multiplication. -30 + 3 + 5 Step 3: Perform the additions from left to right. -27 + 5 Step 4: Perform the final addition. -22 *e) m × (n+p) if m=3, n=2, p=-11 We will show that m × (n+p) = (m × n) + (m × p). Left side: m × (n+p) Step 1: Substitute the given values. 3 × (2 + (-11)) Step 2: Perform the addition inside the parenthesis. 3 × (-9) Step 3: Perform the multiplication. -27 Right side: (m × n) + (m × p) Step 1: Substitute the given values. (3 × 2) + (3 × (-11)) Step 2: Perform the multiplications. 6 + (-33) Step 3: Perform the addition. -27 Since -27 = -27, the property holds. *f) (m × n) + (m × p) if m=7, n=8, p=-9 Step 1: Substitute the given values into the expression. (7 × 8) + (7 × (-9)) Step 2: Perform the multiplications. 56 + (-63) Step 3: Perform the addition. -7 What's next?