If a = 3 and b = -7, find the value of $\frac{5b+(a+b)^2}{(a-b)^2}$

Step 1: Analyze the question We substitute a = 3 and b = -7 into the expression and simplify, being careful with signs.

Step 2: Work out each part

• Numerator: 5b + (a + b)² • 5b = 5(-7) = -35 • a + b = 3 + (-7) = -4, so (a + b)² = 16 • Numerator = -35 + 16 = -19

• Denominator: (a - b)² • a - b = 3 - (-7) = 10 • (a - b)² = 100

Step 3: Divide

Step 4: Answer The value is -0.19, which is option C.

Tip: When a variable is negative, put it in brackets before squaring or subtracting. This avoids the common mistakes of writing a - b = 3 - 7 = -4, or of treating (-4)² as -16. A negative number squared is always positive, but 5b stays negative here.