Question

Subtract and simplify. Show work please!

Answer 1

1) Final expression: $+7y^2-6y-17$

2) Final expression: $21x^3-46x^2+59x-30$

Step-by-step explanation:

1)

The first expression is

$(-2y^2-11y-7)-(-9y^2-5y+10)$

First, we remove the 2nd bracket by changing the sign of all the terms inside:

$-2y^2-11y-7-+9y^2+5y-10$

Now we group the terms with same degree together:

$(-2y^2+9y^2)+(-11y+5y)+(-7-10)$

Now we solve the expression in each brackets:

$(-2y^2+9y^2)+(-11y+5y)+(-7-10)=\\+7y^2-6y-17$

So, this is the final expression.

2)

The second expression is

$(7x-6)(3x^2-4x+5)$

We apply the distributive property, so we rewrite the expression as follows:

$(7x-6)(3x^2-4x+5)=7x(3x^2-4x+5)-6(3x^2-4x+5)$

Solving both brackets,

$7x(3x^2-4x+5)-6(3x^2-4x+5)=\\21x^3-28x^2+35x-18x^2+24x-30$

Now we group terms of same degree together:

$21x^3-28x^2+35x-18x^2+24x-30=\\21x^3+(-28x^2-18x^2)+(35x+24x)-30$

And solving each bracket,

$21x^3+(-28x^2-18x^2)+(35x+24x)-30=\\21x^3-46x^2+59x-30$

So, this is the final expression.

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