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Softa [21]
3 years ago
13

Select all the statements that are true.

Mathematics
1 answer:
alexgriva [62]3 years ago
8 0

Answer:

The product of 8x(5x−6) is 40x^2−48x

The product of (x−3)(5x−6) is 5x^2−21x+18

Step-by-step explanation:

<u><em>Verify each option</em></u>

Part 1) The product of 8x(5x−6) is 40x^2−48x

we have

8x(5x-6)

Applying distributive property

8x(5x)-8x(6)\\40x^2-48x

Compare with the given value

40x^2-48x=40x^2-48x

therefore

The statement is true

Part 2) The product of −4x(2x2+1) is −8x^3−5x

we have

-4x(2x^{2}+1)

Applying distributive property

-4x(2x^{2})-4x(1)\\-8x^3-4x

Compare with the given value

-8x^3-4x \neq -8x^3-5x

therefore

The statement is not true

Part 3) The product of (x−3)(5x−6) is 5x^2−21x+18

we have

(x-3)(5x-6)

Applying distributive property

x(5x)-x(6)-3(5x)+3(6)\\5x^2-6x-15x+18\\5x^2-21x+18

Compare with the given value

5x^2-21x+18=5x^2-21x+18

therefore

The statement is true

Part 4) The product of (2x+3)(x^2+3x−5) is 2x^3+9x^2+9x−25

we have

(2x+3)(x^2+3x-5)

Applying distributive property

(2x)(x^2+3x-5)+(3)(x^2+3x-5)\\(2x^3+6x^2-10x)+(3x^2+9x-15)\\2x^3+9x^2-x-15

Compare with the given value

2x^3+9x^2-x-15 \neq 2x^3+9x^2+9x-25

therefore

The statement is not true

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Step-by-step explanation:

Given the expression

\sqrt{x^2y^3}+2\sqrt{x^3y^4}+xy\sqrt{y}

solving the expression

\sqrt{x^2y^3}+2\sqrt{x^3y^4}+xy\sqrt{y}

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so the expression becomes

\:\sqrt{x^2y^3}+2\sqrt{x^3y^4}+xy\sqrt{y}=xy\sqrt{y}+2xy^2\sqrt{x}+xy\sqrt{y}

Group like terms

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Add similar elements

                                        =2xy^2\sqrt{x}+2xy\sqrt{y}

Therefore, we conclude that:

\sqrt{x^2y^3}+2\sqrt{x^3y^4}+xy\sqrt{y}=2xy^2\sqrt{x}+2xy\sqrt{y}

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