Question

which expression is not equivalent to 6(6 + h)? a} 36 + 6h b} 6h + 36 c} h(6 + 6) d} 3(12 + 2h)

Explanation:

Step1: Expand the original expression

Use the distributive property \(a(b + c)=ab+ac\). Here \(a = 6\), \(b = 6\), \(c=h\), so \(6(6 + h)=6\times6+6h=36 + 6h\).

Step2: Analyze option a

\(36 + 6h\) is equivalent to the expanded - form of \(6(6 + h)\).

Step3: Analyze option b

\(6h+36\) is the same as \(36 + 6h\) due to the commutative property of addition \(a + b=b + a\), so it is equivalent.

Step4: Analyze option c

Expand \(h(6 + 6)=h\times12 = 12h\), which is not equivalent to \(36+6h\).

Step5: Analyze option d

Expand \(3(12 + 2h)=3\times12+3\times2h=36 + 6h\), which is equivalent.

Answer:

C. \(h(6 + 6)\)