BECE Mathematics 2017 Paper

Concept:When multiplying algebraic expressions, multiply the coefficients and add the exponents of the same variables using the laws of indices.Explanation:We need to find the product of $4xy^4$ and $x^2yz$.Recall the index law: $a^m \times a^n = a^{m+n}$.Any variable without a written power has exponent $1$, so $x = x^1$ and $y = y^1$.Write both expressions together:$$4xy^4 \times x^2yz = 4 \times x^1 \times x^2 \times y^4 \times y^1 \times z$$Multiply the $x$-terms using the index law:$$x^1 \times x^2 = x^{1+2} = x^3$$Multiply the $y$-terms:$$y^4 \times y^1 = y^{4+1} = y^5$$The variable $z$ remains unchanged because there is no other $z$ term.Combine everything together:$$4xy^4 \times x^2yz = 4x^3y^5z$$Answer:The correct option is B: $4x^3y^5z$.