Answer:
Therefore
15.
[tex]25c^{2}-9[/tex]
16.
[tex](y+8)(y+1)[/tex]
17.
[tex](x-3y)(x-7y)[/tex]
Step-by-step explanation:
15.
[tex](5c^{2} +3)(5c^{2}-3)[/tex]
Using the Identity (a + b)(a - b) = (a² - b²) we get
Consider here a = 5c and b = 3 then we will have
[tex]((5c)^{2} -(3)^{2})=25c^{2}-9[/tex] .....as required
16.
[tex]y^{2}+9y+8[/tex]
Here Factorize 8 such that sum up to be 9
∴ 8 × 1 = 8 and 8 + 1 =9
[tex]y^{2}+9y+8\\y^{2}+8y+y+8\\y(y+8)+1(y+8)\\(y+8)(y+1)[/tex] ... as required
17.
[tex]x^{2}-10xy+21y^{2}[/tex]
Here Factorize 21 such that sum up to be -10
∴ -3 × -7 = + 21 and -3 - 7 = - 10
[tex]x^{2}-10xy+21y^{2}\\x^{2}-3xy-7xy+21y^{2}\\x(x-3y)-7y(x-3y)\\(x-3y)(x-7y)[/tex] ........as required
Therefore
15.
[tex]25c^{2}-9[/tex]
16.
[tex](y+8)(y+1)[/tex]
17.
[tex](x-3y)(x-7y)[/tex]
