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(4) Pazroxsume sa 1) \( a^{2}-9 \) 2) \( b^{2}+10 b+25 \) 3) \( 25 x^{2}-16 \) 4) \( 9 x^{2}-12 x y+4 y^{2} \) 5) \( 5 a^{2}-20 a b \) 6) \( 7 x^{3}-14 x^{5} \) 7) \( 3 a-3 b+a x-6 x \)

Ask by Nguyen Hanson. in Russia
Jan 24,2025

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Разложите на множители: 1) \( a^{2} - 9 = (a - 3)(a + 3) \) 2) \( b^{2} + 10b + 25 = (b + 5)^{2} \) 3) \( 25x^{2} - 16 = (5x - 4)(5x + 4) \) 4) \( 9x^{2} - 12xy + 4y^{2} = (3x - 2y)^{2} \) 5) \( 5a^{2} - 20ab = 5a(a - 4b) \) 6) \( 7x^{3} - 14x^{5} = 7x^{3}(1 - 2x^{2}) \) 7) \( 3a - 3b + ax - 6x = 3(a - b) + x(a - 6) \)

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The Deep Dive

Let's have some fun factoring these expressions! Here’s a breakdown for each of them: 1) \( a^{2}-9 \) is a classic difference of squares, which factors as \( (a-3)(a+3) \). 2) \( b^{2}+10b+25 \) is a perfect square trinomial and can be factored as \( (b+5)^{2} \). 3) \( 25x^{2}-16 \) is another difference of squares that factors to \( (5x-4)(5x+4) \). 4) For \( 9x^{2}-12xy+4y^{2} \), recognize it as a perfect square trinomial, factoring it into \( (3x-2y)^{2} \). 5) \( 5a^{2}-20ab \) can be factored by taking out the common factor, yielding \( 5a(a-4b) \). 6) In \( 7x^{3}-14x^{5} \), factor out the common term \( 7x^{3} \), resulting in \( 7x^{3}(1-2x^{2}) \). 7) The expression \( 3a-3b+ax-6x \) can be rearranged and factored, giving \( 3(a-b) + x(a-6) \). Happy factoring! Each of these expressions holds unique opportunities to showcase your algebra skills.

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