Question 25 of 43beginner🔍 AnalyzeShort Answer1 mark

Predict what (x + y)(x2x^{2} - xy + y2y^{2}) will be.

Correct Answer

x3x^{3} + y3y^{3}

Exercise: In-text Prediction | Q: 1 | (Page 18)
For More Understanding

Explanation

The textbook provides a list of standard algebraic identities. Among these, the identity for the sum of two cubes is given as x3+y3=(x+y)(x2−xy+y2)x^3 + y^3 = (x + y)(x^2 - xy + y^2). Therefore, the given expression directly matches the right-hand side of this identity, and its predicted value is the left-hand side, which is x3+y3x^3 + y^3.

Solution Steps

  1. Step 1: Refer to the list of algebraic identities studied in the chapter.

  2. Step 2: Locate the identity for the sum of cubes: x3+y3=(x+y)(x2−xy+y2)x^3 + y^3 = (x + y)(x^2 - xy + y^2).

  3. Step 3: Conclude that (x+y)(x2−xy+y2)=x3+y3(x + y)(x^2 - xy + y^2) = x^3 + y^3.

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