How do you find the product $(4 y + 3 z) {(4 y - 3 z)}^{2}$ $(4y+3z)(4y-3z)^2$ ?

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How do you find the product $(4 y + 3 z) {(4 y - 3 z)}^{2}$ $(4y+3z)(4y-3z)^2$ ?

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Answer 1 · 2017-03-25T13:44:04

$(4 y + 3 z) {(4 y - 3 z)}^{2} = 64 y^{3} - 48 y^{2} z - 36 y z^{2} + 27 z^{3}$ $(4y+3z)(4y-3z)^2=color(green)(64y^3-48y^2z-36yz^2+27z^3)$

Explanation:

Using the difference of squares we could write
$(4 y + 3 z) {(4 y - 3 z)}^{2} = (4 y + 3 z) (4 y - 3 z) (4 y - 3 z)$ $(4y+3z)(4y-3z)^2=color(blue)((4y+3z)(4y-3z))(4y-3z)$

$XXXXXXXXXXX = ({(4 y)}^{2} - {(3 z)}^{2}) (4 y - 3 z)$ $color(white)("XXXXXXXXXXX")=color(blue)(((4y)^2-(3z)^2))(4y-3z)$

$XXXXXXXXXXX = (16 y^{2} - 9 z^{2}) (4 y - 3)$ $color(white)("XXXXXXXXXXX")=(16y^2-9z^2)(4y-3)$

Then using the distributive property or tabular multiplication:
${:(underline(xx)," | ",underline(+16y^2),underline(-9z^2)), (+4y," | ",+64y^3,-36yz^2), (underline(-3z),ul(" | "),ul(-48y^2z),ul(+27z^3)), (color(green)(+64y^3),color(green)(-48y^2z),color(green)(-36yz^2),color(green)(+27z^3)) :}$

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How do you find the product $(4 y + 3 z) {(4 y - 3 z)}^{2}$ $(4y+3z)(4y-3z)^2$ ?

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How do you find the product (4y+3z)(4y-3z)^2(4y+3z)(4y−3z)2(4y+3z)(4y-3z)^2?

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How do you find the product $(4 y + 3 z) {(4 y - 3 z)}^{2}$ $(4y+3z)(4y-3z)^2$ ?