Expand the expression (4x + 3y + 5z)^2.

Question

Examoogle · Accepted Answer

The correct answer is Option A: $16x^2 + 9y^2 + 25z^2 + 24xy + 30yz + 40xz$. Verify the individual squared terms first to eliminate incorrect options, then check the cross-term coefficients.

Step-by-Step Solution & Concepts:
Shortcut Trick: Verify the individual squared terms first to eliminate incorrect options, then check the cross-term coefficients.

Formula Used: $$(a + b + c)^2 = a^2 + b^2 + c^2 + 2ab + 2bc + 2ca$$

Given: The expression to expand is $(4x + 3y + 5z)^2$.

Steps: Identify Formula: Use the standard algebraic identity for the square of a trinomial: $(a + b + c)^2 = a^2 + b^2 + c^2 + 2ab + 2bc + 2ca$.. Substitute Values: Substitute $a = 4x$, $b = 3y$, and $c = 5z$ into the identity.. Simplify Terms: Calculate each term individually to get the final expanded polynomial expression.

Answer: A is correct because expanding the expression yields $16x^2 + 9y^2 + 25z^2 + 24xy + 30yz + 40xz$.

Exam Tip: Mastering algebraic expansion identities saves valuable time in RRB and other competitive quantitative aptitude tests.

Examoogle · Answer

Option B: $16x^2 + 9y^2 + 25z^2 + 12xy + 15yz + 20xz$

Examoogle · Answer

Option C: $4x^2 + 3y^2 + 5z^2 + 24xy + 30yz + 40xz$

Examoogle · Answer

Option D: $16x^2 + 9y^2 + 25z^2 + 24xy + 30yz + 20xz$

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