Problem 22
\(4x^2(2x^2+x-5) - x(x^3+5x^2-3) + 17\)
\(4x^2(2x^2)+4x^2(x)+4x^2(-5) - x(x^3)-x(5x^2)-x(-3) + 17\)
\(8x^4+4x^3-20x^2 - x^4-5x^3+3x + 17\)
\(7x^4-x^3-20x^2+3x + 17\)
So the final simplified answer to problem 22 is
\(7x^4-x^3-20x^2+3x + 17\)
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Problem 23
\(-2x(x^3-6x^2+6)+4x^3-(5x^4+10x)\)
\(-2x(x^3)-2x(-6x^2)-2x(6)+4x^3-(5x^4)-(10x)\)
\(-2x^4+12x^3-12x+4x^3-5x^4-10x\)
\(-7x^4+16x^3-22x\)
So problem 23 simplifies to
\(-7x^4+16x^3-22x\)
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Problem 24
\(4b[2a^2-5(3ab-2b^2)]+29ab^2\)
\(4b[2a^2-5(3ab)-5(-2b^2)]+29ab^2\)
\(4b[2a^2-15ab+10b^2]+29ab^2\)
\(4b[2a^2]+4b[-15ab]+4b[10b^2]+29ab^2\)
\(8a^2b-60ab^2+40b^3+29ab^2\)
\(8a^2b-31ab^2+40b^3\)
So problem 24 simplifies to
\(8a^2b-31ab^2+40b^3\)
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Problem 25
\(2y(6x-4x^2y)+13x^2y^2-6\)
\(2y(6x)+2y(-4x^2y)+13x^2y^2-6\)
\(12xy-8x^2y^2+13x^2y^2-6\)
\(12xy+5x^2y^2-6\)
The final answer for problem 25 is
\(12xy+5x^2y^2-6\)
