Question

B. Perform the indicated operations. Simplify your answer.
1. 2ab( 4a² + 3ab - 7b²)
2. -3xy(x³y³ -3x²y + 7xy²) 3. (x + 2) (x² -3x +2)
4. (2x- 1) (2x² + 4x +3)
5. (12y² -9y + 16) (8y³ -14y + 5)

Answer 1

Step-by-step explanation:

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Answer 2

Given:

1. $2ab(4a^{2} +3ab-7b^{2} )$

2.$-3xy(x^{3} y^{3}-3x^{2}y+7xy^{2})$

3.$(x+2)(x^{2}-3x+2)$

4.$(2x-1)(2x^{2}+4x+3)$

5.$(12y^{2}-9y+16)(8y^{3}-14y+5)$

To find: simplified form of equations.

Step-by-step explanation:

Step 1 of 5

Multiply 2ab with all the terms inside the parenthesis.

$2ab(4a^{2} +3ab-7b^{2} )=2ab*4a^{2} +2ab*3ab-2ab*7b^{2}\\\\=8a^{3}b+6^{2}b^{2}-14ab^{3}$

Step 2 of 5

Multiply -3xy with all the terms inside the parenthesis.

$-3xy(x^{3} y^{3}-3x^{2}y+7xy^{2})=-3xy*x^{3} y^{3}+3xy*3x^{2}y-3xy*7xy^{2}\\\\=-3x^{4}y^{4} +9x^{3}y^{2}-21x^{2} y^{3}$

Step 3 of 5

$(x+2)(x^{2}-3x+2)=x(x^{2}-3x+2)+2(x^{2}-3x+2)\\\\=x^{3}-3x^{2} +2x+2x^{2} -6x+4\\\\=x^{3}-x^{2} -4x+4$

Step 4 of 5

$(2x-1)(2x^{2}+4x+3)=2x(2x^{2}+4x+3)-1(2x^{2}+4x+3)\\\\=4x^{3} +8x^{2} +6x-2x^{2}-4x-3\\\\=4x^{3} +6x^{2} +2x-3$

Step 5 of 5

$(12y^{2}-9y+16)(8y^{3}-14y+5)=12y^{2}(8y^{3}-14y+5)-9y(8y^{3}-14y+5)+16(8y^{3}-14y+5)\\\\=96y^{5} -168y^{3} +60y^{2} -72y^{4} +126y^{2} -45y+128y^{3} -224y+80\\\\=96y^{5}-72y^{4} -40y^{3} +186y^{2} -269y+80$