Question 19 of 27beginner🔍 AnalyzeTrue / False2 marks

(a+2)(b+4)=ab+8(a + 2)(b + 4) = ab + 8

Correct Answer

False. The correct expansion is (a+2)(b+4)=ab+4a+2b+8(a + 2)(b + 4) = ab + 4a + 2b + 8. The mistake is missing the middle terms 4a4a and 2b2b that come from multiplying each term in the first bracket by each term in the second bracket.

Exercise: Mind the Mistake, Mend the Mistake | Q: 11 | (Page Page 15)
For More Understanding

Explanation

The chapter shows that (a+b)(c+d)=ac+ad+bc+bd(a + b)(c + d) = ac + ad + bc + bd. Here, (a+2)(b+4)=a⋅b+a⋅4+2⋅b+2⋅4=ab+4a+2b+8(a + 2)(b + 4) = a \cdot b + a \cdot 4 + 2 \cdot b + 2 \cdot 4 = ab + 4a + 2b + 8. The original solution incorrectly omitted the cross terms.

Solution Steps

  1. Apply distributive property: (a+2)(b+4)(a + 2)(b + 4)

  2. =ab+4a+2b+8= ab + 4a + 2b + 8

  3. All four terms must be included

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