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3) \( (2 a+3)^{2} \)

Ask by Weber Lane. in South Africa
Jan 23,2025

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\( (2a + 3)^2 = 4a^2 + 12a + 9 \)

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To expand \( (2a + 3)^{2} \), you can use the formula for squaring a binomial, which is \( (x+y)^{2} = x^{2} + 2xy + y^{2} \). Here, \( x = 2a \) and \( y = 3 \). So, you get \( (2a)^{2} + 2(2a)(3) + (3)^{2} = 4a^{2} + 12a + 9 \). A common mistake when expanding binomials is forgetting to apply the middle term correctly. Remember, the middle term comes from multiplying the two terms and then doubling that product. In this case, always double the product of the outer terms to ensure you capture all components of the expansion!

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