Question

1. expand each expression:
2. (3a - 4b)(3a - b) show your work on the line paper
3. (3a - 4b)(3a - 4b) show your work on the line paper
4. (3a + 4b)(3a - 4b) show your work on the line paper

Explanation:

Step1: Expand using distributive property

For (3a - 4b)(3a - b):
$$(3a)(3a) + (3a)(-b) + (-4b)(3a) + (-4b)(-b)$$

Step2: Calculate each term

$$9a^2 - 3ab - 12ab + 4b^2$$

Step3: Combine like terms

$$9a^2 - 15ab + 4b^2$$

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Step1: Expand using square of difference

For (3a - 4b)(3a - 4b) = $(3a-4b)^2$:
$$(3a)^2 - 2(3a)(4b) + (4b)^2$$

Step2: Calculate each term

$$9a^2 - 24ab + 16b^2$$

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Step1: Expand using difference of squares

For (3a + 4b)(3a - 4b):
$$(3a)^2 - (4b)^2$$

Step2: Calculate each term

$$9a^2 - 16b^2$$

Answer:

1. $9a^2 - 15ab + 4b^2$
2. $9a^2 - 24ab + 16b^2$
3. $9a^2 - 16b^2$