3questions show how you solved the problem 1. subtract & simplify (–y2 – 4y – 8) – (–4y2 – 6y + 3) 2.multiply and simplify 2x2y3z2 · 4xy4x2 3.multiply and simplify (x – 4) (x2 – 5x – 6)

Answers

The answer to the question
1. subtract &  simplify (–y2 – 4y – 8) – (–4y2 – 6y + 3)  2.multiply and simplify 2x2y3z2 · 4xy4

\huge\boxed{8x^5y^7z^2}

Step-by-step explanation:

\text{Use}\ a^n\cdot a^m=a^{n+m}\\\\2x^2y^3z^2\cdot4xy^4x^2=(2\cdot4)(x^2xx^2)(y^3y^4)z^2=8x^{2+1+2}y^{3+4}z^2\\\\=8x^5y^7z^2

1. 3y^2+2y-11

2. 8y^{7}x^{5}z^2

3. x^3-9x^2+14x+24

Step-by-step explanation:

1. We have been given an expression (-y^2-4y-8)-(-4y^2-6y+3) and we are asked to subtract and simplify our given expression.

Using order of operations (PEMDAS), first of all let us remove parenthesis.

-y^2-4y-8+4y^2+6y-3

Now let us group like terms.

(-y^2+4y^2)+(-4y+6y)+(-8-3)

Upon combining like terms our expression simplifies to:

(3y^2)+(2y)+(-11)

3y^2+2y-11

Therefore, our expression simplifies to 3y^2+2y-11.

2. We have been given an expression (2x^2y^3z^2)*(4xy^4x^2) and we are asked to multiply and simplify our given expression.

(2x^2y^3z^2)*(4y^4x*x^2)

(2x^2y^3z^2)*(4y^4x^3)

Using exponent property a^b*a^c=a^{b+c} we will get,

2*4x^{2+3}y^{3+4}z^2

8x^{5}y^{7}z^2

8y^{7}x^{5}z^2

Therefore, our given expression simplifies to 8y^{7}x^{5}z^2.

3. We are asked to multiply and simplify our expression (x-4)(x^2-5x-6).

Using distributive property we will get,

x*x^2-5x*x-6*x-4*x^2-5x*-4-6*-4

x^3-5x^2-6x-4x^2+20x+24

Upon combining like terms we will get,

x^3+(-5x^2-4x^2)+(-6x+20x)+24

x^3+(-9x^2)+(14x)+24

x^3-9x^2+14x+24

Therefore, our given expression simplifies to x^3-9x^2+14x+24.

1)  (-y^2-4y-8+4y^2+6y-3)

2)  32x^5y^4z^2

3)  x^3-9x^2+14x+24

Step-by-step explanation:

Given the expression we have to simplify the expression

1)   (-y^2-4y-8)-(-4y^2-6y+3)

(-y^2-4y-8+4y^2+6y-3)

Combining like terms, we get

3y^2+2y-11

2.)    (2x^2y^3z^2)(4xy.4x^2)

(2x^2y^3z^2)(16x^3y)

32x^5y^4z^2

3.)   (x-4)(x^2-5x-6)

x^3-5x^2-6x-4x^2+20x+24

x^3-9x^2+14x+24



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