Math  /  Algebra

QuestionHomework 1 Directions: Factor each expression complet 1) r216r^{2}-16 3) v225v^{2}-25 5) p24p^{2}-4 7) 9k249 k^{2}-4 9) 3x2273 x^{2}-27 11) 16x23616 x^{2}-36 13) 18a250b218 a^{2}-50 b^{2} 15) a22a+1a^{2}-2 a+1 17) x2+6x+9x^{2}+6 x+9 19) x26x+9x^{2}-6 x+9 21) 25p210p+125 p^{2}-10 p+1 23) 25a2+30ab+9b225 a^{2}+30 a b+9 b^{2} 25) 4a220ab+25b24 a^{2}-20 a b+25 b^{2} 27) 8x224xy+18y28 x^{2}-24 x y+18 y^{2} 29) 8m38-m^{3} 31) x364x^{3}-64 33) 216u3216-u^{3} 35) 125a364125 a^{3}-64 37) 64x3+27y364 x^{3}+27 y^{3} 39) 54x3+250y354 x^{3}+250 y^{3} 41) a481a^{4}-81 43) 16z416-z^{4} 45) x4y4x^{4}-y^{4} 47) m481b4m^{4}-81 b^{4}

Studdy Solution
Factor the expression m481b4m^4 - 81b^4 as a difference of squares.
m481b4=(m29b2)(m2+9b2)=(m3b)(m+3b)(m2+9b2) m^4 - 81b^4 = (m^2 - 9b^2)(m^2 + 9b^2) = (m - 3b)(m + 3b)(m^2 + 9b^2)
Solution: All given expressions have been factored completely.

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