Product of a monomial, square of binomial, sum and difference of two squares and cubes, and problem solving

Example:
𝟐𝒂(𝒎 + 𝒏)
𝟐𝒂(𝒎) + 𝟐𝒂(𝒏)

Example:
𝟒(𝒂 + 𝟐𝒃 + 𝟑𝒄)
𝟒 𝒂 + 𝟒 𝟐𝒃 + 𝟒(𝟑𝒄)

Example:
𝟏𝟎(𝟒𝒎 + 𝟔𝒏 − 𝟖𝟏)
𝟏𝟎 𝟒𝒎 + 𝟏𝟎 𝟔𝒏 − 𝟏𝟎(𝟖𝟏)

Example:
𝒎𝒏(𝟐𝒙 − 𝟑𝒚 − 𝟒𝒛)
𝒎𝒏 𝟐𝒙 − 𝒎𝒏 𝟑𝒚 − 𝒎𝒏(𝟒𝒛)

Example:
𝟐𝒙(𝟓𝒙 𝟑
+ 𝟑𝒙𝒚 − 𝟐𝒚 𝟐
)
𝟐𝒙 𝟓𝒙 𝟐
+ 𝟐𝒙 𝟑𝒙𝒚 − 𝟐𝒙(𝟐𝒚 𝟐
)

QUIZ!
1. 𝟒𝒂 𝟑𝒎 𝟐 − 𝟐𝒏 − 𝟒𝒍 𝟑 + 𝒑
2. −𝟐𝒚𝒙(𝟐𝒂 + 𝟓𝒃 − 𝟑𝒄)
3. 𝟒𝒂 𝟐
𝒃(𝒂 𝟐
+ 𝟐𝒂𝒃 + 𝟑𝒃 𝟐
)
To be
submitted
TODAY!!!!

Example:
𝒂 + 𝟓 (𝒂 − 𝟓)
(𝒂) 𝟐
−(𝟓) 𝟐

Example:
𝟐𝒙 + 𝟏 (𝟐𝒙 − 𝟏)
(𝟐𝒙) 𝟐
−(𝟏) 𝟐

Example:
𝟐𝒙 𝟐
+ 𝟑𝒚 𝟑
(𝟐𝒙 𝟐
− 𝟑𝒚 𝟑
)
(𝟐𝒙 𝟐
) 𝟐
−(𝟑𝒚 𝟑
) 𝟐

QUIZ!
1. (𝒂 + 𝟑)(𝒂 − 𝟑)
2. (𝟐𝒙 + 𝟒)(𝟐𝒙 − 𝟒)
3. (𝟐𝒙 𝟐
− 𝟏)(𝟐𝒙 𝟐
+ 𝟏)
To be
submitted
TODAY!!!!

Example:
(𝟐𝒙 + 𝟑) 𝟐
(𝟐𝒙) 𝟐
+𝟐 𝟐𝒙 𝟑 + (𝟑) 𝟐

Example:
(𝟑𝒙 − 𝟓𝒚) 𝟐
(𝟑𝒙) 𝟐
−𝟐 𝟑𝒙 𝟓𝒚 + (𝟓𝒚) 𝟐

Example:
(𝟒𝒂 + 𝟑𝒃) 𝟐
(𝟒𝒂) 𝟐
+𝟐 𝟒𝒂 𝟑𝒃 + (𝟑𝒃) 𝟐

Example:
(𝟏𝟐 − 𝟓𝒄) 𝟐
(𝟏𝟐) 𝟐
−𝟐 𝟏𝟐 𝟓𝒄 + (𝟓𝒄) 𝟐

QUIZ!
1. (𝟑𝒂 + 𝟒) 𝟐
2. (𝟐𝒙 + 𝟓𝒚) 𝟐
3. (𝟐𝒎 − 𝟕) 𝟐
To be
submitted
TODAY!!!!

Example:
(𝟐𝒙 + 𝟏) 𝟑
(𝟐𝒙) 𝟑
+𝟑(𝟐𝒙) 𝟐
𝟏 + 𝟑(𝟐𝒙)(𝟏) 𝟐
+ (𝟏) 𝟑

Example:
(𝒙 𝟐
+ 𝟐) 𝟑
(𝒙 𝟐
) 𝟑
+𝟑(𝒙 𝟐
) 𝟐
𝟐 + 𝟑(𝒙 𝟐
)(𝟐) 𝟐
+ (𝟐) 𝟑

Example:
(𝟐𝒂 − 𝟒𝒃) 𝟑
(𝟐𝒂) 𝟑
−𝟑(𝟐𝒂) 𝟐
𝟒𝒃 + 𝟑(𝟐𝒂)(𝟒𝒃) 𝟐
− (𝟒𝒃) 𝟑

Example:
(𝟐𝒓 𝟐
− 𝟑) 𝟑
(𝟐𝒓 𝟐
) 𝟑
−𝟑(𝟐𝒓 𝟐
) 𝟐
𝟑 + 𝟑(𝟐𝒓 𝟐
)(𝟑) 𝟐
− (𝟑) 𝟑

QUIZ!
1. (𝒙 + 𝒚) 𝟑
2. (𝟔 + 𝟒𝒅 𝟐
) 𝟑
3. (𝟐𝒙 − 𝟒𝒚 𝟑
) 𝟑
To be
submitted
TODAY!!!!

Example: 𝒂 + 𝒃 (𝒂 + 𝒃)
(𝒂) 𝒂
(𝒂 𝟐
) + (𝒂𝒃) + (𝒂𝒃) + (𝒃 𝟐
)
+ 𝒂 (𝒃) + 𝒃 (𝒂) + 𝒃 (𝒃)

Example: 𝒙 + 𝟒 (𝒙 + 𝟒)
(𝒙) 𝒙
(𝒙 𝟐
) + (𝟒𝒙) + (𝟒𝒙) + (𝟏𝟔)
+ 𝒙 (𝟒) + 𝟒 (𝒙) + 𝟒 (𝟒)

Example: 𝟑𝒙 + 𝟐 (𝟐𝒙 + 𝟒)
(𝟑𝒙) 𝟐𝒙
(𝟔𝒙 𝟐
) + (𝟏𝟐𝒙) + (𝟒𝒙) + (𝟖)
+ 𝟑𝒙 (𝟒)+ 𝟐 (𝟐𝒙) + 𝟐 (𝟒)

Example: 𝒂 − 𝒃 (𝒂 − 𝒃)
(𝒂) 𝒂
𝒂 𝟐
− 𝒂𝒃 − (𝒂𝒃) + (𝒃 𝟐
)
− 𝒂 (𝒃)− 𝒃 (𝒂) + 𝒃 (𝒃)

Example: 𝒃 − 𝟕 (𝒃 − 𝟔)
(𝒃) 𝒃
𝒃 𝟐
− 𝟔𝒃 − (𝟕𝒃) + (𝟒𝟐)
− 𝒃 (𝟔) − 𝟕 (𝒃)+ 𝟕 (𝟔)

Example: 𝟖𝒄 − 𝟒𝒅 (𝟑𝒄 − 𝟐𝒅)
(𝟖𝒄) 𝟑𝒄
𝟐𝟒𝒄 𝟐
− 𝟏𝟔𝒄𝒅 − (𝟏𝟐𝒄𝒅) + (𝟖𝒅 𝟐
)
− 𝟖𝒄 (𝟐𝒅)− 𝟒𝒅 (𝟑𝒄) + 𝟒𝒅 (𝟐𝒅)

Example: 𝒂 − 𝒃 (𝒂 + 𝒃)
(𝒂) 𝒂
𝒂 𝟐
+ 𝒂𝒃 − 𝒂𝒃 − (𝒃 𝟐
)
+ 𝒂 (𝒃) − 𝒃 (𝒂) − 𝒃 (𝒃)

Example: 𝒙 − 𝟑 (𝟐𝒙 + 𝟓)
(𝟐𝒙) 𝒙
𝟐𝒙 𝟐
+ 𝟓𝒙 − 𝟔𝒙 − (𝟏𝟓)
+ 𝒙 (𝟓)− 𝟑 (𝟐𝒙)− 𝟑 (𝟓)

Example:
𝒙 𝟐
− 𝟏 (𝒙 𝟐
+ 𝟑)
(𝒙 𝟐
) 𝒙 𝟐
𝒙 𝟒
+ 𝟑𝒙 𝟐
− 𝟏𝒙 𝟐
− (𝟑)
+ 𝒙 𝟐
(𝟑)− 𝟏 (𝒙 𝟐
)− 𝟏 (𝟑)

QUIZ!
1. 𝟐𝒂 + 𝟑𝒃 (𝟑𝒂 + 𝟐𝒃)
2. (𝟒𝒙 − 𝟑𝒚)(𝟓𝒙 − 𝟔𝒚)
3. (𝟒𝒂 𝟐
+ 𝟐)(𝟑𝒂 𝟐
− 𝟓)
To be
submitted
TODAY!!!!

Find the area of the square with
𝟐𝒙 + 𝟑 dimension.
𝟐𝒙 + 𝟑
Solution:
𝐀 = (𝟐𝒙 + 𝟑) 𝟐
𝐀 = (𝟐𝒙) 𝟐
+ 𝟐(𝟐𝒙)(𝟑) + (𝟑) 𝟐

A rectangular plot measures
𝟑𝒙 + 𝟒 in width and 𝟒𝒙 + 𝟔 in length.
𝟒𝒙 + 𝟔
Solution:
𝐀 = (𝟒𝒙 + 𝟔)(𝟑𝒙 + 𝟒)
𝐀 = 𝟏𝟐𝒙 𝟐 + 𝟏𝟔𝒙 + 𝟏𝟖𝒙 + 𝟐𝟒
𝟑𝒙 + 𝟒

Find the perimeter of
the figure below.
𝟔𝒙 + 𝟏
Solution:
𝑷 = 𝟒(𝟔𝒙 + 𝟏)
𝐏 = 𝟒 𝟔𝐱 + (𝟒)(𝟏)

Find the perimeter of
the figure below.
𝟒𝒙 + 𝟏
Solution:
𝑷 = 𝟐 𝟒𝒙 + 𝟏 + (𝟓𝒙 − 𝟐)
𝐏 = (𝟖𝒙 + 𝟐) + (𝟓𝒙 − 𝟐)
𝟓𝒙 − 𝟐

QUIZ!
1. If a rectangle measures
4x + 3 in length, and
3x + 5 in width, what is
its perimeter?
To be
submitted
on
2. The side of the square is 5x – 3. What is
the area of the square?

Product of a monomial, square of binomial, sum and difference of two squares and cubes, and problem solving

More Related Content

Similar to Product of a monomial, square of binomial, sum and difference of two squares and cubes, and problem solving (20)

More from AjayQuines (20)

Product of a monomial, square of binomial, sum and difference of two squares and cubes, and problem solving