(5m + 6n)² = 25m² + 36n²

Question 12 of 27beginner🔍 AnalyzeTrue / False2 marks

$(5m + 6n)^2 = 25m^2 + 36n^2$

Correct Answer

False. The correct expansion using Identity 1A is $(5m + 6n)^2 = 25m^2 + 60mn + 36n^2$ . The mistake is missing the middle term $2ab$ in the expansion of $(a + b)^2$ .

Exercise: Mind the Mistake, Mend the Mistake | Q: 4 | (Page Page 15)

For More Understanding

Explanation

The chapter presents Identity 1A: $(a + b)^2 = a^2 + 2ab + b^2$ . When squaring a binomial, the middle term $2ab$ must be included. Here, $a = 5m$ and $b = 6n$ , so $2ab = 2(5m)(6n) = 60mn$ .

Solution Steps

Apply Identity 1A: $(a + b)^2 = a^2 + 2ab + b^2$
With $a = 5m$ and $b = 6n$ :
$(5m + 6n)^2 = (5m)^2 + 2(5m)(6n) + (6n)^2$
$= 25m^2 + 60mn + 36n^2$

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