Answer:
1.
A. Product of the sum of binomial
[tex](2a + 5)(2a + 5)[/tex]
[tex](2a) {}^{2} + 2(10a) + 5 {}^{2} [/tex]
[tex] = 4a {}^{2} + 20a + 25[/tex]
B. Product of sum and difference of binomial
[tex](10q - 7)(10q + 7)[/tex]
[tex] (10q) {}^{2} - (7) {}^{2} [/tex]
[tex] = 100q {}^{2} - 49[/tex]
C. Square of difference of binomial
[tex](3a - 2b) {}^{2} [/tex]
[tex](3a - 2b)(3a - 2b)[/tex]
[tex](3a) {}^{2} - 2(6ab) + (2b) {}^{2} [/tex]
[tex] = 9a {}^{2} - 12ab + 4b {}^{2} [/tex]
D. Cube of Binomials
[tex](x - 3)(x {}^{2} + 3x + 9)[/tex]
[tex] = (x - 3) {}^{3} [/tex]
2.
A.
[tex](15 + 4q)(15 - 4q)[/tex]
[tex](15) {}^{2} - 15(4q) + 15(4a) - (4q) {}^{2} [/tex]
[tex]225 - 60q + 60q - 16q {}^{2} [/tex]
[tex] = 225 - 16q {}^{2} [/tex]
B.
[tex](7x {}^{2} - 2) {}^{2} [/tex]
[tex](7x {}^{2} - 2)(7x {}^{2} - 2)[/tex]
[tex](7x {}^{2} ) {}^{2} - 2(14x {}^{2} ) + 2 {}^{2} [/tex]
[tex] = 49x {}^{4} - 28x {}^{2} + 4[/tex]
C.
[tex]( \frac{2}{3} x + \frac{3}{4} y) {}^{2} [/tex]
[tex]( \frac{2}{3} x + \frac{3}{4} y)( \frac{2}{3} x + \frac{3}{4} y)[/tex]
[tex]( \frac{2}{3} x) {}^{2} + 2( \frac{6}{12} xy) + ( \frac{3}{4} y) {}^{2} [/tex]
[tex] = \frac{4}{9} x {}^{2} + \frac{12}{24} xy + \frac{9}{16} y {}^{2} [/tex]
D.
[tex](m + 3n)(m {}^{2} - 3mn + 9n {}^{2} [/tex]
[tex] m(m {}^{2} - 3mn + 9n {}^{2} ) + 3n(m {}^{2} - 3mn + 9n {}^{2} )[/tex]
[tex]m {}^{3} - 3m {}^{2} n + 9mn {}^{2} + 3m {}^{2} n - 9mn {}^{2} + 27n {}^{3} [/tex]
combine similar term
[tex] = m {}^{3} + 27n {}^{3} [/tex]
3.
A.
Given:
Length = (a+4)
Width = (a-4)
A= L×W
Area=
[tex](a + 4)(a - 4)[/tex]
[tex]a {}^{2} - 4a + 4a - 4 {}^{2} [/tex]
[tex] = a {}^{2} - 16[/tex]
B.
Given:
Length = (2x+3y)
V = L×W×H
Volume=
[tex](2x + 3y) {}^{3} [/tex]
[tex](2x) {}^{3} + 3((2x) {}^{2} 3y) + 3(2x(3y) {}^{2} ) + (3y) {}^{3} [/tex]
[tex]8x {}^{3} + 3(12x {}^{2} y) + 3(18xy {}^{2} ) + 27y {}^{3} [/tex]
[tex] = 8x {}^{3} + 36x {}^{2} y + 54xy {}^{2} + 27y {}^{3} [/tex]
