Question

5.2 worksheet

1. $16x^{2}y - 24x^{2}y^{3}$
2. $7a^{2}b - 28ab + 14ab^{2}$
3. $27r^{2}s^{2} - 18r^{3}s^{2} - 36rs^{3}$
4. $3x(x - 4) + 5(x - 4)$

Explanation:

Problem 1: \(16x^2y - 24x^2y^3\)

Step1: Find the GCF of coefficients and variables

The GCF of 16 and 24 is 8. For variables, the GCF of \(x^2y\) and \(x^2y^3\) is \(x^2y\). So factor out \(8x^2y\).
\(16x^2y - 24x^2y^3 = 8x^2y(2 - 3y^2)\) (Note: The original handwritten attempt had a sign error; it should be \(2 - 3y^2\) as \(16\div8 = 2\) and \(-24\div8=-3\))

Step2: Verify the factoring

Multiply \(8x^2y\) with \((2 - 3y^2)\): \(8x^2y\times2 - 8x^2y\times3y^2=16x^2y - 24x^2y^3\), which matches the original expression.

Step1: Find the GCF

The GCF of 7, 28, and 14 is 7. For variables, the GCF of \(a^2b\), \(ab\), and \(ab^2\) is \(ab\). So factor out \(7ab\).
\(7a^2b - 28ab + 14ab^2=7ab(a - 4 + 2b)\)

Step2: Verify

Multiply \(7ab\) with \((a - 4 + 2b)\): \(7ab\times a-7ab\times4 + 7ab\times2b = 7a^2b-28ab + 14ab^2\), which is correct.

Step1: Find the GCF

The GCF of 27, 18, and 36 is 9. For variables, the GCF of \(r^2s^2\), \(r^3s^2\), and \(rs^3\) is \(rs^2\). So factor out \(9rs^2\).
\(27r^2s^2 - 18r^3s^2 - 36rs^3=9rs^2(3r - 2r^2 - 4s)\)

Step2: Verify

Multiply \(9rs^2\) with \((3r - 2r^2 - 4s)\): \(9rs^2\times3r-9rs^2\times2r^2 - 9rs^2\times4s=27r^2s^2 - 18r^3s^2 - 36rs^3\), which is correct.

Answer:

\(8x^2y(2 - 3y^2)\)

Problem 2: \(7a^2b - 28ab + 14ab^2\)