1) Factors of [tex]c^2+6c+9[/tex]are [tex](c+3)(c+3)[/tex]
2) Factors of [tex]16x^2+48xy+36y^2[/tex] are [tex](4x+6y)^2[/tex]
3) Factors of [tex]25a^2-70a + 49[/tex] are [tex](5a-7)^2[/tex]
4) Factors of [tex]16ax + 4x^2 +16a^2[/tex] are [tex](2x+4a)^2[/tex]
5) Factors of [tex]25a^2 +9b^2 + 30ab[/tex] are [tex](5a+3b)^2[/tex]
6) Factors of [tex]2x^2 - 16x + 32[/tex] are[tex]2(x-4)^2[/tex]
7) Factors of [tex]5c^2 +30c + 45[/tex] are [tex]5(c+3)^2[/tex]
8) Factors of [tex]128x^2 +96xy + 18y^2[/tex] are [tex]2(8x+3y)^2[/tex]
9) Factors of [tex]450a^2 +242c^2 + 660ac[/tex] are [tex]2(15a+11c)^2\\[/tex]
10) Factors of [tex]a^8 - 12a^4 + 36[/tex] are [tex](a^4-6)^2[/tex]
11) Factors of[tex]9x^2 - y^2[/tex] are [tex](3x-y)(2x+y)[/tex]
12) Factors of [tex]16a^2 - 4b^2[/tex] are [tex](4a+2b)(4a-2b)[/tex]
13) Factors of [tex]1-4y^2[/tex] are [tex](1-2y)(1+2y)[/tex]
14) Factors of [tex]a^2 - c^2[/tex] are [tex](a-c)(a+c)[/tex]
15) Factors of [tex]x^6-36[/tex] are [tex](x^3-6)(x^3+6)\\[/tex]
16) Factors of [tex]a^2b^2 - d^2[/tex] are [tex](ab-d)(ab+d)[/tex]
17) Factors of [tex]9x^4y^2 - z^6[/tex] are [tex](3x^2y-z^3)(3x^2y+z^3)[/tex]
18) Factors of [tex]36x^2y^6 - 16[/tex] are [tex](6xy^3-4)(6xy^3+4)[/tex]
19) Factors of [tex]0.09y^2 - 0.81[/tex] are [tex](0.03y-0.9)(0.03y+0.9)[/tex]
20)Factors of [tex]1-100x^2[/tex] are [tex](1-10x)(1+10x)[/tex]
21) Factors of [tex]36a^2 - b^2[/tex] are [tex](6a-b)(6a+b)[/tex]
22) Factors of [tex]9x^2-16[/tex]are [tex](3x-8)(3x+8)[/tex]
Step-by-step explanation:
1) [tex]c^2+6c+9[/tex]
[tex]c^2+6c+9\\=c^2+3c+3c+9\\=c(c+3)+3(c+3)\\=(c+3)(c+3)[/tex]
2) [tex]16x^2+48xy+36y^2[/tex]
[tex]=16x^2 +48xy + 36y^2\\=(4x)^2+2(4x)(6y)+(6y)^2\\=(4x+6y)^2[/tex]
3) [tex]25a^2-70a + 49[/tex]
[tex]25a^2 - 70a + 49\\=(5a)^2-2(5a)(7)+(7)^2\\=(5a-7)^2[/tex]
4) [tex]16ax + 4x^2 +16a^2[/tex]
[tex]4x^2+16ax+16a^2\\=(2x)^2+2(2x)(4a)+(4a)^2\\=(2x+4a)^2[/tex]
5) [tex]25a^2 +9b^2 + 30ab[/tex]
[tex]25a^2 +9b^2 + 30ab\\=25a^2+30ab+9b^2\\=(5a)^2+2(5a)(3b)+(3b)^2\\=(5a+3b)^2[/tex]
6) [tex]2x^2 - 16x + 32[/tex]
[tex]2x^2 - 16x + 32\\Taking\,\,2\,\,common:\\=2(x^2-8x+16)\\=2((x)^2-2(x)(4)+(4)^2)\\=2(x-4)^2[/tex]
7) [tex]5c^2 +30c + 45[/tex]
[tex]Taking\,\,5\,\,common:5(c^2+6c+9)\\=5((c)^2+2(c)(3)+(3)^2)\\=5(c+3)^2[/tex]
8) [tex]128x^2 +96xy + 18y^2[/tex]
[tex]128x^2 +96xy + 18y^2\\Taking\,\,2\,\,common:\\=2(64x^2+48xy+9y^2)\\=2((8x)^2+2(8x)(3y)+(3y)^2)\\=2(8x+3y)^2[/tex]
9) [tex]450a^2 +242c^2 + 660ac[/tex]
[tex]450a^2 +242c^2 + 660ac\\Taking\,\,2\,\,common:\\=2(225a^2+121c^2+330ac)\\=2((15a)^2+(11c)^2+2(15a)(11c))\\=2(15a+11c)^2\\[/tex]
10)[tex]a^8 - 12a^4 + 36[/tex]
[tex]a^8 - 12a^4 + 36\\=(a^4)^2-2(a^4)(6)+(6)^2\\=(a^4-6)^2[/tex]
11) [tex]9x^2 - y^2[/tex]
[tex]9x^2 - y^2\\=(3x)^2-(y)^2\\=(3x-y)(2x+y)[/tex]
12) [tex]16a^2 - 4b^2[/tex]
[tex]16a^2 - 4b^2\\=(4a)^2-(2b)^2\\=(4a+2b)(4a-2b)[/tex]
13) [tex]1-4y^2[/tex]
[tex]1-4y^2\\=(1)^2-(2y)^2\\=(1-2y)(1+2y)[/tex]
14) [tex]a^2 - c^2[/tex]
[tex]a^2 - c^2\\=(a)^2-(c)^2\\=(a-c)(a+c)[/tex]
15) [tex]x^6-36[/tex]
[tex]x^6-36\\=(x^3)^2-(6)^2\\=(x^3-6)(x^3+6)\\[/tex]
16) [tex]a^2b^2 - d^2[/tex]
[tex]a^2b^2 - d^2\\=(ab)^2-(d)^2\\=(ab-d)(ab+d)[/tex]
17) [tex]9x^4y^2 - z^6[/tex]
[tex]9x^4y^2 - z^6\\=(3x^2y)^2-(z^3)^2\\=(3x^2y-z^3)(3x^2y+z^3)[/tex]
18) [tex]36x^2y^6 - 16[/tex]
[tex]36x^2y^6 - 16\\=(6xy^3)^2-(4)^2\\=(6xy^3-4)(6xy^3+4)[/tex]
19) [tex]0.09y^2 - 0.81[/tex]
[tex]0.09y^2 - 0.81\\=(0.03y)^2-(0.9)^2\\=(0.03y-0.9)(0.03y+0.9)[/tex]
20) [tex]1-100x^2[/tex]
[tex]1-100x^2\\=(1)^2-(10x)^2\\=(1-10x)(1+10x)[/tex]
21) [tex]36a^2 - b^2[/tex]
[tex]36a^2 - b^2\\=(6a)^2-(b)^2\\=(6a-b)(6a+b)[/tex]
22) [tex]9x^2-16[/tex]
[tex]9x^2-16\\=(3x)^2-(8)^2\\=(3x-8)(3x+8)[/tex]
